What is the 3-4-5 rule?

A triangle with sides of 3, 4 and 5 units has a right angle between the 3 and the 4, because 3² + 4² = 5². Measure 3 ft along one line and 4 ft along the other, and the corner is square when the diagonal between the two marks reads exactly 5 ft.

What are the angles of a 3-4-5 triangle?

90, 53.13 and 36.87 degrees. The angle opposite the 4 side is 53.13 and the angle opposite the 3 side is 36.87, for every multiple of the triangle.

What multiples of 3-4-5 can I use?

Any: 6-8-10, 9-12-15, 12-16-20 and so on. Use the largest one the space allows, because the same tape error on a bigger triangle throws the corner out by less. 1/8 in on a 3-4-5 ft triangle is about 1 in out over 20 ft; on 12-16-20 it is about a quarter inch. The US Army's FM 5-426 teaches it as 6-8-10 and says never to start below 6 ft.

How do I square a building or foundation?

Measure both diagonals of the rectangle. When they are equal, every corner is square. For a 24 by 36 ft foundation both should read 43 ft 3 3/16 in. This calculator gives the diagonal for any length and width.

Does the 3-4-5 rule work in inches or meters?

Yes. The rule is a ratio, so 30-40-50 cm or 18-24-30 in are square just the same.

What if my diagonal is too long?

The corner is open, wider than 90 degrees. A short diagonal means it is closed. Enter how far off it reads and the calculator gives the actual angle and how far the end of the wall is out.

Home › Framing › 3-4-5 Rule Calculator

3-4-5 Rule Calculator

FM 5-426 squaring methods, with the tape error worked out

Three feet one way, four feet the other, and the corner is square when the diagonal reads exactly five. That part everybody knows. What nobody says is how much a small tape error costs: on a 3-4-5 triangle, 1/8 in on the diagonal leaves a 20 ft wall about an inch out of line at its far end. On 12-16-20 it is a quarter of that. This calculator gives the diagonal for any two sides and shows the error that comes with it.

The two sides

Side A

Side B

Wall length to check (how far the corner will be carried)

Your diagonal is off by (plus if long, minus if short, zero to skip)

Measure both sides from the corner. For a rectangle, enter its length and width: both diagonals must read the value below.

Specification summary

Generated from on . Reopen that address to reproduce these figures exactly.

Entered

Result

The corner, the two sides and the diagonal

Worked example

The classic triangle, 3 ft and 4 ft, carried along a 20 ft wall.

Diagonal. √(3² + 4²) = √25 = 5 ft 0 in.
Angles. 90, 53.13 and 36.87 degrees.
Tape error. 1/8 in on a 60 in diagonal turns the corner by 0.249 degrees, which is 1.04 in out at the end of a 20 ft wall.

Scale the same triangle to 12-16-20 and the same 1/8 in costs a quarter of that.

The formula

Pythagoras for the diagonal, and its derivative for the error:

diagonal = √(A² + B²) angle error ≈ diagonal × tape error ÷ (A × B)

A, B: the two sides from the corner
tape error: how far the diagonal reading is off, in the same units
angle error: in radians; multiply by 57.3 for degrees

Out of line at a wall end = wall length × tan(angle error).

Where the numbers come from

The diagonal is Pythagoras and the error is the first derivative of the law of cosines. Every figure the calculator returns can be checked with a calculator.

The method is the US Army's: FM 5-426, Carpentry (1995), Chapter 4, which teaches squaring lines by the 6-8-10 and diagonal methods and sets a 6 ft minimum. This page adds the numbers behind that minimum.

Use the biggest triangle that fits

The 3-4-5 rule works at any scale, and the scale is not cosmetic. A tape reading is off by the same amount whatever the triangle, so a bigger triangle turns the same reading error into a smaller angle.

What 1/8 in of tape error on the diagonal does to the corner, and to the end of a 20 ft wall
Triangle	Corner out by	20 ft wall end out by
3-4-5 ft	0.249°	1.04 in
6-8-10 ft	0.124°	0.52 in
9-12-15 ft	0.083°	0.35 in
12-16-20 ft	0.062°	0.26 in
15-20-25 ft	0.050°	0.21 in

The US Army's carpentry manual, FM 5-426, reaches the same conclusion without the arithmetic. It teaches the method as 6-8-10, not 3-4-5, and says plainly: "For accuracy, never start with a measurement of less than 6 feet." For a 50 by 100 ft layout it uses 12-16-20. The table above is why.

Doubling the triangle halves the error. On a deck or a slab, where the corner is carried 20 ft or more, the 3-4-5 ft triangle is the least accurate way to use the rule. Pull 12-16-20, or measure the two diagonals of the whole rectangle.

Squaring a rectangle: the two diagonals

For a foundation, a deck frame or a shed floor, the rectangle checks itself. If the two diagonals are equal, every corner is square. If they are not, the long diagonal runs to the corners that are open.

Enter the length and width above and the calculator gives the diagonal both should read. A 24 by 36 ft foundation should measure 43 ft 3 3/16 in on both diagonals.

The diagonal method catches a mistake the 3-4-5 triangle cannot: a parallelogram. Four sides can all be the right length with every corner wrong, and only the diagonals disagree.

The angles of a 3-4-5 triangle

The two angles that are not the right angle are 53.13 and 36.87 degrees. They are the same for every multiple, 6-8-10 or 30-40-50, because scaling a triangle does not change its angles.

That is also why the rule works on a roof: a 9 in 12 pitch is a 3-4-5 triangle, rise 9 over run 12 with a rafter of 15, which is 36.87 degrees.

Frequently asked questions

What is the 3-4-5 rule?: A triangle with sides of 3, 4 and 5 units has a right angle between the 3 and the 4, because 3² + 4² = 5². Measure 3 ft along one line and 4 ft along the other, and the corner is square when the diagonal between the two marks reads exactly 5 ft.
What are the angles of a 3-4-5 triangle?: 90, 53.13 and 36.87 degrees. The angle opposite the 4 side is 53.13 and the angle opposite the 3 side is 36.87, for every multiple of the triangle.
What multiples of 3-4-5 can I use?: Any: 6-8-10, 9-12-15, 12-16-20 and so on. Use the largest one the space allows, because the same tape error on a bigger triangle throws the corner out by less. 1/8 in on a 3-4-5 ft triangle is about 1 in out over 20 ft; on 12-16-20 it is about a quarter inch. The US Army's FM 5-426 teaches it as 6-8-10 and says never to start below 6 ft.
How do I square a building or foundation?: Measure both diagonals of the rectangle. When they are equal, every corner is square. For a 24 by 36 ft foundation both should read 43 ft 3 3/16 in. This calculator gives the diagonal for any length and width.
Does the 3-4-5 rule work in inches or meters?: Yes. The rule is a ratio, so 30-40-50 cm or 18-24-30 in are square just the same.
What if my diagonal is too long?: The corner is open, wider than 90 degrees. A short diagonal means it is closed. Enter how far off it reads and the calculator gives the actual angle and how far the end of the wall is out.

Check these numbers yourself

FM 5-426 Carpentry, Chapter 4, Building Layout and Foundation: Squaring LinesHeadquarters, Department of the Army, 1995, public domain. Page 4-5 gives the 6-8-10 method, its multiples such as 12-16-20 for a 50 by 100 ft layout, the rule never to start with a measurement under 6 ft, and the diagonal method for rectangles. Read 2026-09-26.

How every figure here is verified: Sources & Method. Who builds this: Lucas Pradella, and the method is on About. Found something wrong? Tell us and it gets fixed or removed.

Figures on this page last checked against the source documents on 2026-09-26. Codes are amended locally; confirm against the edition your jurisdiction enforces.

Related calculators

Geometry only. The result is as good as the tape and the marks it is read between.