Three Documents, One Paddock, No Agreement
A roadside paddock changes hands. The conveyance recites five acres more or less. The county mapping portal, asked politely, returns 1.95 hectares. The fencing contractor who walked it on Tuesday has quoted against just under two hundred thousand square feet, and the seed merchant wants a rate per thousand square feet that nobody has converted yet. Four numbers, one field, and every one of them defensible in the document it came from.
None of them is wrong. They are measuring different outlines. The deed runs to the middle of the road because that is what the original conveyance did and nobody has changed it since. The mapping polygon stops at the made-up edge of the highway, because that is where the surveyed detail is. The contractor measured inside the stock fence, which stands back from the highway boundary by whatever the original fencer thought reasonable, and then took a flank strip off again because a drainage easement runs down it and he will not put a post in it. Each subtraction is small. Together they are seven per cent of the field.
So the work here is not conversion. Conversion is exact arithmetic with published factors and it takes ten seconds. The work is establishing which outline each number describes, converting all of them into one unit so they can be laid side by side, and then deciding — explicitly, in writing, before anyone prices anything — which outline the job is being bought, fenced and seeded against. Get that order the wrong way round and you convert three incompatible figures into three incompatible figures in a tidier unit.
Which Acre, and Whose Foot
There is one acre in current use and its size is not a matter of convention or region. Since the international yard and pound agreement of 1959 — published on this side by the National Bureau of Standards as Refinement of Values for the Yard and the Pound — the yard has been 0.9144 metres exactly, which makes the foot 0.3048 m exactly, the square foot 0.09290304 m², and the acre of 43,560 square feet 4,046.8564224 m² exactly. Not approximately. That figure terminates. An American acre and a British acre are the same acre, and have been for longer than most people on site have been alive. The historical oddities — the Irish plantation acre, the Scots acre, the Cheshire acre — are dead units that turn up only in old deeds, and a deed old enough to use one is a deed to hand to a surveyor rather than to a tape.
The hectare is easier still, because it was defined to be easy: 10,000 m² exactly, one square hectometre, listed in the BIPM SI Brochure among the non-SI units accepted for use with the SI. That is why hectare arithmetic never needs a lookup and acre arithmetic always does. Shifting a decimal point converts hectares to square metres; nothing shifts to convert acres.
The one genuine trap is the US survey foot, which is 1200/3937 m rather than 0.3048 m — longer by about two parts in a million. Areas carry that error twice, so a survey acre is about four parts in a million larger than an international acre: roughly 0.016 m² on the acre, or one and a half square metres across a hundred-acre farm. That is nothing on a fence quote and everything in a coordinate system, which is why it survives at all. NIST and NOAA published a joint notice in 2020 deprecating the US survey foot from the end of 2022, and it now persists only where a state's own legislation names it for its State Plane zone. If a plat carries coordinates in feet, the plat has to say which foot; if it does not say, the surveyor who drew it does.
Convert once, early, into whichever unit the majority of the paperwork already uses, and write the factor you used on the sheet. The reason is not arithmetic difficulty — it is that a number converted twice by two people using two rounded factors comes back different, and then somebody spends an afternoon deciding which of two nearly-identical figures is the real one.
| From | To | Factor | Where it comes from |
|---|---|---|---|
| 1 acre | square metres | 4,046.8564224 exactly | 43,560 ft² at the 1959 international foot of 0.3048 m |
| 1 acre | square feet | 43,560 exactly | Definitional — one chain by one furlong, 66 ft × 660 ft |
| 1 acre | hectares | 0.40468564224 exactly | Follows from the two above; a hectare is 2.4710538 acres |
| 1 hectare | square metres | 10,000 exactly | A square hectometre, accepted for use with the SI |
| 1 hectare | square feet | 107,639.104 (to three decimals) | 10,000 ÷ 0.09290304, and it does not terminate |
| 1 square metre | square feet | 10.7639104 (to seven decimals) | 1 ÷ 0.09290304 — the one factor worth memorising |
Put each of the three figures through it in turn and read all four units at once, so the deed, the mapping and the quote end up on one line in one unit before anybody argues about which is right.
The land area value you want to convert.
The unit your input value is currently measured in.
Equivalent in acres
1 acre
- Hectares
- 1 acre
- Square feet
- 43,560 sq ft
- Square meters
- 4,046.86 m²
They open the calculator with your figures already in it
Land Area Converter: 1 acre — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
Estimated cost — your price
This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.
What this calculation does not cover
- Every entry is turned into acres first and the other three units are derived from that acre figure, so a hectares-to-square-metres reading travels through the acre factor rather than through the 10,000 m² that defines a hectare.
- The hectare factor is stored as 0.404685642 while the square-foot and square-metre factors are stored in full, so a hectare value sent through the page and back returns about six parts in ten billion off what was typed — nothing on a parcel, but the two routes do not agree digit for digit.
- Only acres, hectares, square feet and square metres are offered; a deed, title plan or overseas listing quoting square yards, square miles, roods or perches has to be converted before its number can be entered here.
- The value box is capped at 100,000 whichever unit is selected, so the ceiling is a number rather than an area — 100,000 acres in one setting and 100,000 square feet, about 2.3 acres, in another — and anything typed above it is pulled back to the cap when the field loses focus.
- Nothing in the arithmetic separates a plan area from the ground surface beneath it, so a figure taken off a sloping site converts unit for unit while the real surface remains larger than all four numbers shown.
- The headline answer is the acre figure whichever direction you are working in, with hectares, square feet and square metres carried on the breakdown rows below it, so a metric reader takes their result off a row rather than off the result line.
The Line on the Plan Has a Thickness
Before the area is worth computing, settle how well the boundary is actually known, because the area inherits every bit of that uncertainty and then squares it. In England and Wales the registered title plan is, under section 60 of the Land Registration Act 2002, a general boundary: it shows the general position of the boundary and expressly does not fix its exact line unless somebody has gone to the trouble of a determined boundary application. HM Land Registry Practice Guide 40 spells out what the plan does and does not represent, and the answer includes the area — the register does not guarantee it.
Title plans are drawn on Ordnance Survey base mapping at 1:1250 in towns, 1:2500 over most rural ground and 1:10000 on moorland. A plotted line half a millimetre wide covers 0.625 m of ground at 1:1250 and 1.25 m at 1:2500. Take a one-hectare square and move all four sides outward by half a metre — comfortably inside the thickness of the line at rural scale — and you have gained 201 m², two per cent of the field, without anybody drawing anything differently. That is the honest resolution of a title plan area, and it is why the same document that shows you the shape declines to certify the size.
In the United States the equivalent question is what standard the survey was performed to. A boundary survey performed under the 2021 Minimum Standard Detail Requirements for ALTA/NSPS Land Title Surveys is a document with a stated precision behind it, and the area on that plat means something. A deed call copied forward through four conveyances since 1911 is not the same animal. Neither is a parcel polygon from a county GIS layer, which is a mapping product assembled for taxation and lookup and usually carries a disclaimer saying exactly that.
Where the deed itself is the only evidence, remember the ordinary order of precedence when its parts disagree: natural monuments first, then artificial monuments, then the courses and distances written out, and area last. The recited quantity is the weakest call in the description. This is what more or less is doing in a metes-and-bounds recital — it is not decoration, it is a statement that the acreage is descriptive rather than operative, and that the monuments on the ground control. A deed whose calls do not close cannot have a correct recited area, and a deed that closes to one part in several thousand still leaves an area figure with real width on it.
There is a second boundary that has nothing to do with the register. Where a parcel abuts a highway or a watercourse, the ordinary presumption in England and Wales is that title runs to the middle line — ad medium filum — unless something rebuts it, and comparable centreline presumptions exist across most US states with their own local qualifications. A deed area computed on that basis includes ground you will never fence, never seed and never build on. Establish which side of that line your figure sits on before you convert it, not after.
Only a Rectangle Multiplies
Length times width is exact for a rectangle and for nothing else. That is not pedantry, because the failure mode is not random: averaging the two long sides and the two short sides and multiplying almost always over-reads, and it over-reads in the direction that makes a buyer feel good and a contractor bid short.
Take a plain trapezoidal field — a hundred metres along the road, sixty at the back, eighty metres deep, symmetric. Its true area is the mean of the parallel sides times the depth: 6,400 m², or 1.581 acres. Now do it the quick way. The two slanting flanks each measure 82.46 m along the ground, so the mean length is 80 m, the mean width is 82.46 m, and the product is 6,597 m² — 1.630 acres. You have invented 197 m² out of nothing but a reasonable-sounding average, which is three per cent, and on this shape the error is invisible to the eye because all four measured dimensions are correct.
The way out is decomposition, and it is old, dull and reliable. Cut the parcel into rectangles and right-angled triangles whose sides you can actually put a tape on, compute each piece, and add. Where the boundary wanders, run one long straight base line down the middle of the plot, step along it at fixed intervals, and measure the perpendicular offset to the boundary at each station — the strip between two stations is a trapezoid and the whole side sums as one. Where the surveyor has already given you corner coordinates, the area by coordinates method in any surveying text, Ghilani and Wolf's Elementary Surveying among them, closes the polygon in one pass and does not care how many sides it has.
Any of those beats a satellite-image area tool used without reading what it computed. A mapping application may return a geodesic area on the ellipsoid or a planar area on whatever projection the map is drawn in, and those are different numbers. Conformal projections — Transverse Mercator, UTM, State Plane, the Ordnance Survey National Grid — preserve shape and deliberately do not preserve area. The National Grid's central meridian scale factor of 0.9996 squares to an area factor of 0.9992, which quietly removes 800 m² from every hundred hectares near that meridian. Ordnance Survey's A Guide to Coordinate Systems in Great Britain and NOAA Manual NOS NGS 5 for the State Plane system both set out how the scale factor varies across a zone; the practical rule is that a computed area from a map is only as trustworthy as your knowledge of what it was computed on.
- Walk the boundary once before measuring anything, marking every corner the tape will have to reach and every place the line changes direction.
- Draw the parcel roughly to shape on paper and cut it into rectangles and right-angled triangles, keeping the pieces large and few.
- Measure each piece horizontally, stepping the tape in level bays on any run that falls, since a tape lying on a slope reads long.
- Compute each piece separately, in one unit, and write the piece dimensions down rather than only the answers.
- Add the pieces, then check the total against any figure on the deed or the plan and account for the difference rather than splitting it.
- Record which outline your total describes — to the road centreline, to the highway boundary, or inside the fence.
Offsets at a fixed interval along a baseline, added as trapezoids or by Simpson's rule, or a surveyor's corner coordinates closed in one pass — the two routes this section gives for a boundary that is not a rectangle. The field above, entered as its two parallel sides at its depth apart, gives back the true area rather than the averaged one.
Offsets for a wandering edge measured off a straight line; coordinates for a plot with a survey.
Trapezoidal treats the edge as straight between stations; Simpson's rule fits a curve through them.
The fixed distance along the baseline between one offset and the next.
How many offsets you took, including the first and the last; the fields after that count are ignored.
The distance square off the baseline to the edge at station 1.
The distance square off the baseline to the edge at station 2.
The distance square off the baseline to the edge at station 3.
The distance square off the baseline to the edge at station 4.
The distance square off the baseline to the edge at station 5.
The distance square off the baseline to the edge at station 6.
The distance square off the baseline to the edge at station 7.
The distance square off the baseline to the edge at station 8.
The distance square off the baseline to the edge at station 9.
The distance square off the baseline to the edge at station 10.
The distance square off the baseline to the edge at station 11.
Area
274.6 ft²
The trapezoidal rule joins each pair of offsets with a straight line. On an edge that bows outward it reads slightly low, which Simpson's rule, shown beside it, corrects.
- Baseline length
- 58.5 ft
- Area by the trapezoidal rule
- 274.63 ft²
- Area by Simpson's rule
- 273.54 ft²
They open the calculator with your figures already in it
Irregular Area Calculator (Offsets and Coordinates): 275 ft² — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
Estimated cost — your price
This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.
What this calculation does not cover
- A plane area. A plot on a slope has a larger surface than its plan area, and the plan area is the one a deed, a planning form and most prices use.
- Offsets assume the edge runs straight or smoothly between stations. A corner or a sudden change between two stations is missed; put a station at every corner.
- Coordinates from a map or a projected grid carry that grid's scale factor, which changes area slightly across a zone; a survey's own coordinates on a site grid do not.
The Map Is Flat and the Field Is Not
Every area on every deed, plan and register is a horizontal area — the parcel's shadow, projected onto a level plane. Nothing about that is negotiable and nothing about it changes with the terrain. Two farms of identical registered acreage, one flat and one draped over a hillside, are the same size in law, in tax and in the price per acre.
The ground disagrees. Grass, topsoil, mulch, geotextile, erosion matting and hydroseed all lie on the surface, and a sloping surface is longer than its projection by exactly one over the cosine of the slope angle. On a gentle fall the correction is a rounding error. On a bank it stops being one: a hectare of mapped ground at one in four presents 1.031 hectares of surface to cover, and at one in two it presents 1.118 hectares. Order to the map figure on a steep site and you are short by an amount that is entirely predictable and entirely your own fault.
The same factor applies to anything that runs along the ground rather than sitting on it. A fence line crossing that one-in-four bank needs 3.1 per cent more wire, netting and rail than its plan length suggests, and the post spacing set out on the drawing lands short of the far corner. Where the seed rate and the fence run both come off the map without correction, the two shortfalls arrive on the same day.
| Grade | Angle | Surface ÷ plan | Extra per mapped hectare | Extra per mapped acre |
|---|---|---|---|---|
| 5% (1 in 20) | 2.86° | 1.0012 | 12 m² | 5 m² (0.001 ac) |
| 10% (1 in 10) | 5.71° | 1.0050 | 50 m² | 20 m² (0.005 ac) |
| 20% (1 in 5) | 11.31° | 1.0198 | 198 m² | 80 m² (0.020 ac) |
| 25% (1 in 4) | 14.04° | 1.0308 | 308 m² | 125 m² (0.031 ac) |
| 33% (1 in 3) | 18.43° | 1.0541 | 541 m² | 219 m² (0.054 ac) |
| 50% (1 in 2) | 26.57° | 1.1180 | 1,180 m² | 478 m² (0.118 ac) |
Subtracting the Parts Nobody Will Work In
Gross parcel area and net workable area are two different quantities that share a name in casual speech, and in valuation practice they are defined terms rather than opinions — a UK valuer's versions come from RICS guidance, not from the deed. What comes off between the two is site-specific and rarely small: the highway strip if the deed runs to the centreline, the verge the highway authority will not release, a utility wayleave, a drainage or sewer easement that no post and no foundation may enter, the ditch and its maintenance strip, hardstanding that is staying, the yard around a building, and any protected ground fixed by an arboricultural report.
Measure each of those as its own shape, in its own right, with its own dimensions written down. This matters more than it sounds. A single deduction figure carried in somebody's head is unauditable, and it is the first thing to be forgotten when the drawing changes; six named pieces on a sheet can each be revisited when the easement turns out to be four metres rather than three. Long thin strips are the ones that surprise people — a four-metre easement down a two-hundred-metre flank is 800 m², a fifth of an acre, from a strip nobody would think to call significant.
Be equally careful about what you are not entitled to subtract. Ground you cannot build on is often still ground you must clear, mow, fence and pay tax on. A grazing paddock's fence follows the title boundary even where a wayleave runs inside it; a seeding rate applies to the whole sward including the strip over the sewer. Different trades subtract different things from the same parcel, which is exactly why the takeoff sheet should carry the gross figure and each named deduction rather than one net number with no working.
Agricultural support schemes add a further definition again, measuring eligible area from orthophotography with ineligible features taken out on their own rules, and that figure will not match either the deed or your fence line. Treat it as a fourth number rather than as a correction to the first three.
This one takes rectangles, circles and triangles up to a hundred metres a side — roughly three hundred and twenty-eight feet — which is the scale of the pieces you are subtracting rather than the parcel you are subtracting them from. Run the yard, the hardstanding and the turning circle here and take the results off the gross; a strip longer than that cap — the easement down the paddock flank is 193.5 m — either splits into two pieces or comes off the tape as one multiplication.
Pick the shape that best matches your area.
The longer side of the rectangle.
The shorter side of the rectangle.
Total area
149.5 ft²
- Square feet
- 149.5 sq ft
- Square yards
- 16.61 sq yd
- Acres
- 0 ac
They open the calculator with your figures already in it
Square Footage Calculator: 150 ft² — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
Estimated cost — your price
This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.
What this calculation does not cover
- Area is taken from the outline of one shape with nothing subtracted: there is no field for a kitchen island, a chimney breast, a stair opening or a structural column, so anything standing inside the measured outline is still counted as floor.
- The number returned is bare geometry with no waste, cut or overage percentage folded into it, so material ordered straight off it leaves nothing for off-cuts, pattern match or breakage.
- Two horizontal measurements multiplied give a plan area, so a pitched roof plane, a ramped driveway or a lawn falling away from the house carries more real surface than the figure shown.
- Circle mode squares half the diameter, so a tape reading two per cent out moves the answer by roughly four, and one diameter can only describe a true circle rather than an oval pond or the curve of a bay window.
- Base times height, halved, is taken on trust: nothing checks that the height was measured at a right angle to the base, so the slanted edge entered by mistake inflates the result with no warning.
- Every length field stops at 100 m (about 328 ft), which caps the acres line near 2.47 acres (1 hectare) for a rectangle and lower for the other two shapes, so a paddock or lot beyond that has to be measured in sections and totalled by hand.
Fence Runs on Perimeter, and Perimeter Does Not Follow From Area
The single most expensive assumption on a rural parcel is that knowing the acreage tells you the fencing. It does not, and the gap is not marginal. One hectare as a square is 100 m by 100 m and closes with 400 m of fence. The same hectare as a roadside strip 20 m deep runs 500 m long and closes with 1,040 m. As a circle — the minimum for any shape at all — it closes with 354 m. Identical area, identical price per acre, and the fencing bill varies by a factor of nearly three.
So measure the perimeter as a measurement, not as a derivation. Walk the line, record each straight run separately with its own length, and note where the run changes direction, because corners are where the strainer posts, the stays and the labour concentrate. A parcel with eleven sides costs meaningfully more to fence than a rectangle enclosing the same ground, and the difference lives entirely in the corner assemblies rather than in the wire.
Then apply the slope correction from the previous section to any run that climbs, add the gates where they are actually wanted rather than where they are drawn, and check whether the fence follows the title boundary or stands back from it. On the paddock at the top of this article the deed rectangle has a 600 m perimeter to the road centreline, while the fence line inside the highway boundary runs 587 m. Thirteen metres is not the point; knowing which of the two your quote covers is.
How Many Decimals You Have Actually Earned
A converter will hand back nine significant figures because the factors are exact, and every digit past the fourth or fifth is a claim about the boundary that no boundary supports. The third decimal place of an acre is 4.05 m² — a square two metres on a side. A tape read to the nearest decimetre along a 200 m by 100 m parcel carries about 30 m² of doubt on its own, which lands in the second decimal of the acre, and a general-boundaries title plan is an order of magnitude vaguer than that.
Publish two decimals of an acre or four of a hectare for anything measured with a tape and a wheel; three and five respectively only when there is a survey behind it with a stated precision. Round once, at the end, from the full-precision figure rather than from an already-rounded intermediate, and state the unit and the outline alongside the number every single time — 4.78 acres inside the fence and 4.94 acres to the road centreline are both true, and only one of them is what the machine is being booked for.
| Digit | In square metres | In square feet | Roughly |
|---|---|---|---|
| 0.1 acre | 404.7 m² | 4,356 ft² | A tennis court and a half |
| 0.01 acre | 40.5 m² | 436 ft² | A two-car garage |
| 0.001 acre | 4.05 m² | 43.6 ft² | A square two metres on a side |
| 0.01 hectare | 100 m² | 1,076 ft² | A ten-metre square |
| 0.001 hectare | 10 m² | 108 ft² | A parking bay |
| 1,000 ft² | 92.9 m² | 1,000 ft² | 0.023 acres — the unit US seed rates use |
Putting the Three Numbers on One Line
Back to the paddock. Measured to the road centreline it is 100 m of frontage by 200 m deep — 20,000 m², which is 2.0000 hectares, 4.942 acres and 215,278 square feet, and which is why the conveyance says five acres more or less. The mapping polygon clips at the highway boundary five metres in from the centreline and returns 1.95 hectares. The stock fence stands a further 1.5 m back and there is a four-metre drainage easement down one flank. Every figure below is the same field.
Written out that way the disagreement stops being a disagreement. Each row is a different outline, each subtraction has a named cause, and the seven per cent between the top row and the bottom is fully accounted for rather than split down the middle. That table is what goes on the takeoff sheet, and what gets sent to the seed merchant with the row circled.
One last conversion earns its place on a mixed-unit job, because it is the one people get wrong under time pressure: a seeding rate of one pound per thousand square feet is 4.88 grams per square metre, 48.8 kilograms per hectare, or 43.56 pounds per acre. Take the rate from the supplier's own label rather than from memory, convert it once, and apply it to the surface area from the slope table rather than to the plan area from the deed.
- Name each figure by the document it came from and the outline it describes, before converting anything.
- Convert every figure into one unit using the exact factors, and record the factor used.
- Lay them side by side and account for each difference with a named cause — centreline, verge, easement, fence setback.
- Decide which outline the job is bought, fenced and seeded against, and mark it on the sheet.
- Apply the slope factor to anything that covers or crosses the ground, and leave the title area alone.
- Round once at the end, to two decimals of an acre or four of a hectare unless a survey says you may do better.
| Outline | Square metres | Hectares | Acres | Square feet |
|---|---|---|---|---|
| Deed, to the road centreline | 20,000 | 2.0000 | 4.942 | 215,278 |
| Mapping polygon, clipped at the highway boundary | 19,500 | 1.9500 | 4.819 | 209,896 |
| Inside the stock fence | 19,350 | 1.9350 | 4.781 | 208,282 |
| Workable, after the 4 m drainage easement | 18,576 | 1.8576 | 4.590 | 199,950 |
What to settle before the parcel becomes a price
Six things that all get decided with a tape, a title plan and one conversion, and all get expensive the moment somebody prices the wrong outline. The workspace opens on the 200 m by 100 m paddock from the last section — replace both dimensions with your own.
- Which outline every figure describes — Road centreline, highway boundary, fence line or workable ground. Four legitimate answers on one field, seven per cent apart on the paddock above.
- One unit, converted once, with the factor written down — An acre is 4,046.8564224 m² exactly and a hectare is 10,000 m² exactly. Two people rounding differently produce two figures and an afternoon of arguing about which is real.
- How well the boundary is known before the area is computed — A general-boundaries title plan at 1:2500 plots a line 1.25 m wide. Half a metre on all four sides of a hectare is 201 m², and the register does not guarantee the area anyway.
- The parcel cut into rectangles and triangles, not averaged — Mean length times mean width over-reads on almost any irregular shape — three per cent on a plain trapezoid whose four measured dimensions are all correct.
- Slope correction on everything that lies on or crosses the ground — Seed, topsoil, matting and fence wire follow the surface; deeds, tax and price per acre follow the horizontal projection. One in four is 3.1 per cent, one in two is 11.8.
- Perimeter measured, never derived from the area — One hectare closes with 354 m of fence as a circle, 400 m as a square and 1,040 m as a 20 m strip. Count the corners too — that is where the strainers and the labour go.
Opens the calculators above on one screen with the dimensions from this article already filled in. Quantities only — this site publishes no price list, because local prices vary too much to publish honestly.