Short answer: The 3/4/5 rule checks a right angle by measuring 3 along one line, 4 along the other, and 5 across the gap. What the rule does not tell you is how good that check was. Take the two short sides as true and the diagonal as off by one millimetre: on a triangle drawn at 300 × 400 × 500 mm that millimetre means the corner is 0.24° out, and on one drawn at 3 × 4 × 5 m it means 0.024°. Ten times the triangle, a tenth of the angle.
The definition is easy to find; Google prints it above the results. This page is about what follows from the same arithmetic: for a given length discrepancy, the angle it represents depends on how large you drew the triangle — and nothing in the reading tells you which case you are in.
1. The rule, and the inverse that makes it a check
Mark 3 units along your first line and 4 along your second. If the corner is a true right angle, the diagonal between the marks reads exactly 5. It is the smallest whole-number case of a2 + b2 = c2, and it holds in any unit as long as all three use the same one.
What makes it a check is the inverse. If the diagonal does not read 5, the check has not passed; and if the two short sides are true and the diagonal really is off, the size of the discrepancy says how far from square the corner is. Holding the two short sides a and b fixed and working near a right angle, a small change in the diagonal c moves the included angle by about c ÷ ab radians per unit of c. That is one radian per 2.4 m on a 3 × 4 × 5 m triangle, so one millimetre is 0.024 degrees — and one radian per 0.24 m on a 300 × 400 × 500 mm one, where the same millimetre buys ten times the angle.
2. The same millimetre, four triangles
Every row assumes the two short sides are true and only the diagonal is off, by one millimetre. The last column is that angle projected across three metres.
| Triangle drawn at | Diagonal | 1 mm on the diagonal | Projected across 3 m |
|---|---|---|---|
| 300 × 400 × 500 mm | 0.5 m | 0.239° | 12.5 mm |
| 1.5 × 2 × 2.5 m | 2.5 m | 0.048° | 2.5 mm |
| 3 × 4 × 5 m | 5 m | 0.024° | 1.25 mm |
| 6 × 8 × 10 m | 10 m | 0.012° | 0.63 mm |
Those are linearised figures and they survive exact solution. A diagonal one millimetre short or long on the 300 × 400 × 500 mm triangle gives −0.2385° and +0.2390°, projecting to −12.488 mm and +12.513 mm. On the 3 × 4 × 5 m triangle the exact pair is −1.2499 mm and +1.2501 mm.
The ten-to-one comparison in the opening is between those two specific rows: a triangle ten times longer in every side, read with the same one-millimetre discrepancy. It is not a general rule about tape measures.
3. Which errors this actually covers
One millimetre on the diagonal alone is a deliberately narrow case. In general all three lengths carry error, and near a right angle the angle moves with all three — to first order, in radians:
δC ≈ (c δc − a δa − b δb) ÷ ab
Two consequences cut against the instinct that a longer triangle is simply safer. An error in either short side pulls the angle the opposite way to one in the diagonal, so errors of the same sign partly cancel. And a tape whose graduations are proportionally long or short scales all three sides by the same factor, leaving the angle exactly unchanged — it distorts your dimensions without touching your squareness. A fixed offset added to all three readings does not have that property; only a proportional one does.
A length being wrong and a reading being wrong are also different. If the diagonal genuinely is 5.001 m, the corner is obtuse by the amount in the table. If it is true and the tape merely reads 5.001, nothing is out until you act on it — and moving the line to bring the reading back to 5.000 introduces the error in the opposite direction.
4. What the projected figure is, and what it is not
Take a straight wall and a set-out grid whose boundary line runs at angle θ to it. Measure the distance L along the grid direction, and measure the gap between grid and wall perpendicular to that same grid direction. Under those two conditions the gap changes by L × tan θ. So 12.5 mm at three metres is a difference between two ends: if the gap is 90 mm where you start and the wall opens away from the grid, it is about 102.5 mm three metres on; if it closes in, about 77.5 mm.
It is not the width of any cut piece — that depends on where you set the first line. It does not survive a change of reference: pace L along the wall instead of along the grid and you are measuring a different span. And it is not a statement about the room: the angle between your two set-out lines, the angle of a wall to your grid, and the rotation of the whole grid are three different variables, and the check speaks only to the first.
5. What the check cannot see
Three limits, and they are separate.
It squares two lines to each other, not to the room. A grid that is perfectly square inside a room that is not still meets the walls at an angle. You gain a deliberate geometry to work from instead of an inherited one — not a guarantee about where the resulting taper ends up, which depends on the room and on where the grid sits in it.
How much angle a given discrepancy represents is set by the size you drew. For the same absolute discrepancy on the diagonal, a smaller triangle converts it into a proportionally larger angle — and the reading looks identical either way.
It is three lengths on a plane. That says nothing about whether the surface is flat, whether a wall is plumb, or whether a floor falls. A wall can satisfy 3/4/5 and still be bowed. Squareness and flatness are different properties, checked differently.
6. What none of this settles
No product record on this site describes a room's squareness, a substrate, a starting line or a cut. What to confirm before choosing lists which questions the product records answer, the one-third rule for tiles covers how narrow an end cut is left, what a quote should list covers where set-out sits in a scope of works, and three rooms worked through covers the quantity side.
Questions people ask
What is the 3/4/5 rule for tiling?
Measure 3 units along one line and 4 along the other; if the diagonal between the marks is exactly 5, the corner is a right angle. Any unit works as long as all three match. It is used to establish a square set-out before the first tile goes down.
Is the 345 method foolproof?
No, for three separate reasons. It squares your two lines to each other but not to the walls. Its precision depends on the size you draw it at — for the same one-millimetre discrepancy on the diagonal, the 300 × 400 × 500 mm triangle gives ten times the angular error of the 3 × 4 × 5 m one. And three lengths on a plane say nothing about flatness, plumb or fall.
What measurements should I use for the 3/4/5 rule?
Any multiple works. Holding the absolute discrepancy fixed, a larger triangle converts it into a smaller angle — on the figures in section 2, doubling every side halves the angle that a one-millimetre diagonal discrepancy represents. What limits the choice in practice is the space available and whether the tape can be held true over the longer spans, since a longer run is also easier to sag or skew.
Where these numbers come from
The angular and projected figures are arithmetic on the 3-4-5 triangle, under the stated condition that the two short sides are exact and only the diagonal varies by one millimetre; section 2 gives both the linearised and the exactly solved values. They are not readings taken from a room and have not been checked against a laid floor. The expression in section 3 is the first-order form near a right angle, in radians. The description of the rule matches the summary Google printed above its Australian results for the phrase on 19 September 2026. Nothing here is a specification for your project: what to confirm before choosing lists what the product records do and do not settle, and a sample is the way to see a face before committing to it.
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