Developed Length: the Run That Is Longer Than the Distance

A slope is longer than its shadow

A run that rises as it travels is longer than the distance it covers on plan, by a factor that depends only on the slope. That is the whole of the first case, and it is the one most often skipped because the plan drawing is the drawing everybody has.

The magnitudes are worth carrying. A roof at six in twelve is 11.8% longer up the slope than across the plan. At twelve in twelve it is 41.4% longer. A one-in-twelve ramp is only 0.35% longer, which is why ramp lengths are quoted as plan distances and rafter lengths never are — the correction is negligible at one extreme and dominant at the other, and the habit follows the trade.

The same factor applies to anything laid on the slope: battens, flashings, cable runs, a stair stringer. It does NOT apply to what is measured horizontally on the same structure — the going of a stair, the plan length of a ramp — and mixing the two within one calculation is the error the factor exists to prevent.

A bend is shorter than the corner it replaces

This one is counter-intuitive and it costs material in the wrong direction every time it is guessed. A right-angled bend of a given radius does NOT add to the run — it takes away from it.

Set it out. Two straight legs meeting at a square corner run from tangent point to tangent point in two steps of one radius each: 2r in total. The arc that replaces them is a quarter circle, which is π⁄2 times the radius, or about 1.571r. So the bend is about 0.43 radii SHORTER than the square corner, per bend.

On a small-radius bend in a light conduit, that is a few millimetres and nobody cares. On a large-radius bend in heavy cable containment, where the radius may be several hundred millimetres because the cable demands it, four or five bends in a run remove a meaningful length — and a take-off that adds the tangent lengths and then adds an arc on top has counted the corner twice.

The practical rule is to work in TANGENT POINTS rather than corners. Measure the straights between where the bending starts and stops, then add each bend's arc. That is what the conduit-bend page asks for, and it is why it asks for the straights separately.

A helix unrolls into a straight line

A spiral stair's stringer, a coiled pipe, a helical cable wrap — all of them are the same construction. Cut the cylinder they wind around and roll it flat, and the helix becomes the hypotenuse of a right triangle: one side is the total rise, the other is the circumference multiplied by the number of turns.

That is genuinely all of it, and it makes an awkward three-dimensional measurement into the same square root as the sloping run above. It also explains why a spiral stair's stringer is so much longer than its height suggests: at a typical radius, one full turn contributes several metres of circumference against a rise of perhaps two, so the developed length is dominated by the going rather than by the height.

The same unrolling is why a helical stringer can be fabricated from straight stock and rolled, and why the flat pattern is the drawing the fabricator actually wants.

Where it fails: the length is not the input, the ratio is

For a ramp or a ladder, the length is an OUTPUT of a constraint rather than a thing to be measured. An accessible ramp has a maximum slope; a ladder has a required setting angle. The rise is given, the ratio is given, and the length follows — so entering a length here is answering a question the code has already decided.

This matters because the two constraints behave differently when a job is tight. A ramp that will not fit at its maximum slope does not become a steeper ramp; it becomes a longer ramp with a landing in it, and the landings have their own dimensions that the slope calculation knows nothing about. A ladder that will not reach at its correct angle does not get leaned further back; it becomes a taller ladder or a different access method.

So the developed length these pages give is a minimum against one constraint, and the thing that usually governs in practice is the space available, the landings, or the headroom at the top. Every one of them says which constraint it applied.

Where it fails: an equivalent length is not a length

Three of the calculators on this list return a figure measured in metres or feet that MUST NOT be ordered against, and the distinction is the most valuable thing on this page.

A fitting's equivalent length is a statement about PRESSURE LOSS: an elbow resists flow about as much as some stated length of straight pipe of the same size would. It is a device for adding a fitting's resistance into a friction calculation, and the number has no physical existence — the elbow is a few centimetres long and its equivalent length may be a couple of metres.

Order pipe against a total that includes equivalent lengths and the order is wildly over. Size a pump against a total that omits them and the pump is under. The two totals are for two different questions and they should never appear in the same column: the site's pages label them explicitly, and the equivalent-length pages say in as many words that the result is for sizing and not for buying.

The same trap sits in flexible duct. Its equivalent length depends on how much it is compressed, so the same physical run has a different equivalent length depending on installation quality — a length that varies with workmanship is obviously not a quantity anyone can order.

The alternative: walk it with a wheel

For anything that already exists, the alternative to computing a developed length is measuring one along the actual path — a measuring wheel round a curve, a tape following a slope, a string line pulled through a duct route. It captures every bend, sag and deviation the drawing does not have.

The computed figure earns its place before the thing exists: a conduit route being priced, a stringer being ordered, a ramp being checked for fit. Its value is that it is transparent about which geometry it assumed, so that the difference from the wheel can be explained rather than absorbed.

Where the two disagree materially, the usual cause is neither the arithmetic nor the tape: it is that the installed route is not the drawn route. That is worth knowing early, and it is the reason these pages report what they assumed rather than only what they computed.