Example 1
- Side A: 3
- Side B: 4
- Side C: 5
The layout forms a right angle
This is the basic pattern that gives the method its name.
3-4-5 ratio calculator
Type two legs and the hypotenuse. The calculator checks whether a² + b² sits close to c². The 3, 4, 5 triple closes a right angle. Doubled 6, 8, 10 does too. At 3.05, 4.0, and 5.0 the layout is not perfectly square, and the millimeter tolerance shows it.
The 3-4-5 rule is one of the simplest ways to set out a right angle without advanced equipment. This calculator helps you quickly check whether given lengths match a right triangle, or how close they are to the correct proportion. Related: slope percent, stair step height.
Results
Side a (m), Side b (m), Hypotenuse c (m) and Tolerance (mm). The result shows up here.
How the results are calculated
The 3-4-5 ratio checks a right angle on site. The formula is a² + b² ≈ c², the Pythagorean theorem. With a tolerance in mm, |c − √(a²+b²)| must stay inside that limit. Scaling 3-4-5 by n suggests sides when you want a larger triangle with the same corner.
A string triangle 3, 4, and 5 m squares a slab or a deck frame. Doubled 6, 8, and 10 works too, because it is the same triple twice. Typing 3.05, 4.0, and 5.0 already misses a perfect corner: five centimeters too much on the short side at zero tolerance. On a 3 by 4 m wall the hypotenuse should be 5.00 m, not 4.90.
Type side a, side b, and hypotenuse c in meters. Tolerance in mm and the scale factor are optional. Empty tolerance leaves a strict compare. A comma in 3.05 works like 3,05.
Stair riser height is next door: 2.8 m and 16 steps is 17.50 cm, a different formula. A 0.6 on 6 m driveway is 10% and 5.71°. Ridge height takes roof pitch, not a 3-4-5 string.
A stretched tape or a crooked stake hurts c more than a. A 5 mm tolerance on five meters is a looser wall; 1 mm is closer to trim work. The calculator does not set the corner for you, it only says whether three numbers hold the angle.
Type 3, 4, and 5, click Calculate, and see a right angle. Then 6, 8, and 10. Finally 3.05, 4, and 5: the layout is not perfectly square.
How to use this calculator
- Type side a and side b in meters, the two sides that should meet at a right angle, for example 3 and 4.
- Enter hypotenuse c, for example 5. That is the diagonal between the free ends of a and b.
- Optionally set a tolerance in mm when the tape does not need to be perfect to the millimeter.
- Click Calculate. 3, 4, and 5 close a right angle. 3.05, 4, and 5 already fail a strict tolerance.
- Stairs and slope percent sit next door. This page stays a Pythagoras check.
a, b, and c on a 3-4-5 layout
The calculator checks whether a² + b² sits close to c². The 3, 4, 5 triple closes a right angle on site. Doubled 6, 8, 10 does too.
- a
- First side, meters. 3 with b = 4 and c = 5 closes the angle. 3.05 with 4.0 and 5.0 fails the millimeter tolerance.
- b
- Second side. 4 in the 3-4-5 triple. 8 in the 6-8-10 double also passes.
- c
- Hypotenuse. 5 with 3 and 4, or 10 with 6 and 8. A square-check on site, not solving a missing side on Pythagoras.
Example scenarios
Example 2
- Side A: 6
- Side B: 8
- Side C: 10
The layout forms a right angle
The rule works not only for 3-4-5 itself, but for any proportional multiple of those lengths.
Example 3
- Side A: 3.05
- Side B: 4.0
- Side C: 5.0
The layout is not perfectly square
This is a practical field example where a small deviation shows that the setup still needs adjustment.
Example 4
- Side a (m): 3
- Side b (m): 4
- Hypotenuse c (m): 5
The layout forms a right angle
What is the 3-4-5 rule? Sides 3, 4 and 5 close a right angle, because 9 + 16 = 25.
Related calculators
FAQ
Do 3, 4, and 5 make a right angle?
Yes. 3² + 4² = 9 + 16 = 25, and 5² is 25. The first card confirms it.
Do 6, 8, and 10 work too?
Yes. That is the 3-4-5 triple doubled. 36 + 64 = 100.
What about 3.05, 4.0, and 5.0?
The layout is not perfectly square. The short side is 5 cm too long for a clean 3-4-5.
What tolerance in mm should I set?
A wall or slab often allows a few millimeters. Trim work sits nearer 1-2 mm. Empty tolerance leaves a strict compare.
What should c be when a = 3 m and b = 4 m?
Exactly 5 m. At 3 and 6 m, c = √(9+36) ≈ 6.708 m, which is no longer a clean 3-4-5.
What is the 3-4-5 scale for?
It multiplies the triple. Scale 2 gives 6-8-10. Scale 0.5 gives 1.5-2-2.5 on a small frame.
Does a 17.50 cm stair count here?
No. Riser height is on the stair page. Here you have three triangle sides.
Is a 10% slope the same angle?
A 0.6 on 6 m slope is 10% and 5.71°, another calculator. 3-4-5 looks for 90°, not a grade percent.
Do the units have to be meters?
All three sides in the same unit. 3, 4, and 5 feet also close the angle, as long as you do not mix feet with meters.
What if c is empty?
The calculator needs three sides to compare. Without c there is nothing to set against √(a²+b²).
Knowledge sources
Volume and waste come from the sizes you type. Below are volume and NIST SI units.
Page updated in 2026.