SettingsSettings for this calculationUS
The side you hold fixed, measured from the corner: usually the longer side, or the one set off an existing wall.
Set out from a line you trust — the face of the existing house, a boundary offset, a string between two profiles — and measure this side along it from the corner peg. Most layouts take the long side as the base, because an angular error at the corner grows along whichever side is longest.
Tools needed: Tape measure, String line and pins
The second side, running from the same corner and meant to be square to the base line.
Measured from the same corner point as the base side, to the mark at its far end. For a rectangle it is the width; for a single corner, such as a deck frame against a house, it is the length of the side that has to come off the base at a right angle.
A single diagonal across one corner, or the two diagonals of a four-cornered layout.
With one corner pegged — the first corner of a slab, a frame against a wall — measure across from the end of the base side to the end of the other side and enter it. Once all four corners are pegged, measure corner to corner both ways and enter how much longer one diagonal is than the other: that difference finds a racked layout without needing the sides to be exactly the lengths drawn.
The tape reading from the end of the base side straight across to the end of the other side.
Pull the tape between the same two marks the sides were measured to, level, and read it to the finest division you can. The page compares it with the square figure and works out the corner angle and how far the far end has to move.
Diagonal when square
30.79 ft
The diagonal reads longer than the square figure, so the corner is open — more than 90° — and the far end of the second side has to swing towards the far end of the base line by the distance in the last row. Swing it on the tape from the corner so the side keeps its length, then read the diagonal again; two or three rounds of swinging and re-reading usually settle it.
- Squaring triangle: leg along the longer side
- 20 ft
- Squaring triangle: leg along the shorter side
- 15 ft
- Squaring triangle: diagonal between the two marks
- 25 ft
- Measured diagonal less the square figure
- 2.48 in
- Angle at the corner
- 90.85 °
- Corner out of square by
- 0.85 °
- Move the far end of the second side by
- 2.94 in
They open the calculator with your figures already in it
Squaring Calculator for Layout and Setting Out (3-4-5 Rule): 30.79 ft — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
Show calculation logicHide calculation logic
How this was calculated
Formula source(s)
- Euclid, Elements, Book I, Proposition 48 (D. E. Joyce's edition, Clark University): if the square on one side of a triangle equals the squares on the other two together, the angle between those two is right — which is why any multiple of 3, 4 and 5 makes a square corner — and Proposition 47, its converse, which gives the expected diagonal √(a² + b²)
- The QUIKRETE Companies, Layout Basics for Slabs and Footers: stake out with the 3-4-5 triangular method, any multiple such as 6-8-10 or 9-12-15 giving the same result, then double-check for squareness by measuring the diagonals between opposite corners, which should be equal; batter boards set back from the work keep the lines
- NIST Digital Library of Mathematical Functions, §4.42 Solution of Triangles, the law of cosines (4.42.5): the corner angle from its two sides and the diagonal across it, and, applied to the two halves of a parallelogram, d₁² + d₂² = 2(a² + b²) and d₁² − d₂² = 4ab·cos θ, from which the racked shift and angle follow
Inputs used
- Side Along the Base Line
- 26 ft
- Side to the Far Corner
- 16.5 ft
- How You Are Checking
- One diagonal, across the corner
- Diagonal You Measured
- 31 ft
- Difference Between the Two Diagonals
- 0.67 in
Intermediate steps
- Squaring triangle: leg along the longer side
- 20 ft
- Squaring triangle: leg along the shorter side
- 15 ft
- Squaring triangle: diagonal between the two marks
- 25 ft
- Measured diagonal less the square figure
- 2.48 in
- Angle at the corner
- 90.85 °
- Corner out of square by
- 0.85 °
- Move the far end of the second side by
- 2.94 in
Confidence note: The diagonal reads longer than the square figure, so the corner is open — more than 90° — and the far end of the second side has to swing towards the far end of the base line by the distance in the last row. Swing it on the tape from the corner so the side keeps its length, then read the diagonal again; two or three rounds of swinging and re-reading usually settle it.
What this calculation does not cover
- Every figure here is a horizontal distance. A tape laid on sloping ground reads the slope, which is longer than the plan distance, so on a falling site take the sides and the diagonals in level steps or along a level line; otherwise the diagonal disagrees with the square figure on a corner that is in fact square.
- Take every reading with the same tape, at the same pull and from the same marks — the centre of the pin or the nail in the profile, not the edge of a peg. Two tapes, or one tape pulled differently, can disagree by more than the error being looked for.
- The single-diagonal check assumes the two side lengths were measured from the same corner point to the same two marks the diagonal runs between. If the sides are not the lengths entered, the corner angle and the offset describe a different corner.
- Equal diagonals prove a rectangle only together with equal opposite sides, and the two-diagonal shift assumes that the opposite sides are equal — that the shape has racked as a parallelogram rather than been pegged at four independent wrong lengths.
- The 3-4-5 triangle shown is the largest that fits on the two sides from the corner. A bigger one is better still: if the lines can be pegged long past the corners, scale the triangle up beyond the building and mark the legs on the lines themselves, never in the air.
- No tolerance is applied. How far out a corner may be is set by the job's specification or the tolerance standard it follows; the page reports the error and leaves the judgement to that.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-10-05 · v1.0.0
Regulatory standards & verification citations3
- Euclid, Elements, Book I, Proposition 48 (D. E. Joyce's edition, Clark University): if the square on one side of a triangle equals the squares on the other two together, the angle between those two is right — which is why any multiple of 3, 4 and 5 makes a square corner — and Proposition 47, its converse, which gives the expected diagonal √(a² + b²)
- The QUIKRETE Companies, Layout Basics for Slabs and Footers: stake out with the 3-4-5 triangular method, any multiple such as 6-8-10 or 9-12-15 giving the same result, then double-check for squareness by measuring the diagonals between opposite corners, which should be equal; batter boards set back from the work keep the lines
- NIST Digital Library of Mathematical Functions, §4.42 Solution of Triangles, the law of cosines (4.42.5): the corner angle from its two sides and the diagonal across it, and, applied to the two halves of a parallelogram, d₁² + d₂² = 2(a² + b²) and d₁² − d₂² = 4ab·cos θ, from which the racked shift and angle follow
Cite this page
Your workspace
Most jobs need more than one number. Add the calculators you need next and they open right here, underneath this one — your figures stay on screen and nothing is lost to a page change.