Example 1
- Side a: 3
- Side b: 4
- Hypotenuse c: 5
Layout forms a right angle
Do 3, 4, and 5 make a right angle? 3² + 4² = 25 = 5² → yes (90°).
3-4-5 Ratio Calculator
Enter two legs and the hypotenuse. The calculator checks whether a² + b² is close to c². The 3, 4, 5 triple closes a right angle. Doubled 6, 8, 10 does too. At 3.05, 4, and 5 the c gap is about 30 mm with empty tolerance.
Results
Side a (m), Side b (m), Hypotenuse c (m) and Tolerance (mm). The result shows up here.
A fast string check for a right angle with 3-4-5. Slope percentage is on the slope percent page. Related: stair step height.
How the results are calculated
a3
b4
c5
90°yes
The 3-4-5 ratio calculator checks a right angle on site with the Pythagorean theorem. The formula is a² + b² ≈ c². Expected hypotenuse is √(a² + b²). With a tolerance in mm, |c − √(a²+b²)| must stay inside that limit. Scaling 3-4-5 by n suggests sides for 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 36 + 64 = 100. At 3.05, 4, and 5 expected c ≈ 5.030 m, so the gap versus 5.0 m is about 30 mm with empty tolerance. On a 3 by 4 m wall the hypotenuse should be 5.00 m, not 4.90.
Enter side a, side b, and hypotenuse c in the header unit. Tolerance in mm and the scale factor are optional. Empty tolerance means a strict relative compare. A comma in 3.05 works the same as a period.
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 uses 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.
Enter 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
- Enter side a and side b in the header unit — 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 (gap ≈ 30 mm).
- Stairs and slope percent sit next door. This page stays a Pythagoras check.
Formula
a² + b² ≈ c² · expected c = √(a² + b²)
With tolerance: |c − √(a²+b²)| ≤ tolerance [mm] / 1000
3, 4, 5 → right angle. 6, 8, 10 → right angle. 3.05, 4.0, 5.0 → gap ≈ 30 mm.
a, b, and c on a 3-4-5 layout
The calculator checks whether a² + b² is close to c². The 3, 4, 5 triple closes a right angle on site. Doubled 6, 8, 10 does too.
- a
- First side in the header unit. 3 with b = 4 and c = 5 closes the angle. 3.05 with 4 and 5 leaves about a 30 mm gap.
- 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 against √(a²+b²).
- tol
- Tolerance in mm. An empty value means a strict relative a²+b² ≈ c² compare.
Example scenarios
Example 2
- Side a: 6
- Side b: 8
- Hypotenuse c: 10
Layout forms a right angle
Scale 2 → 6-8-10. 6² + 8² = 100 = 10².
Example 3
- Side a: 3.05
- Side b: 4
- Hypotenuse c: 5
Layout is not a perfect right angle
At 3.05 / 4 / 5 expected c ≈ 5.030 m; gap vs 5.0 m ≈ 30 mm.
Related calculators
Frequently asked questions
How do I check a right angle with the 3-4-5 rule?
Measure sides a and b plus hypotenuse c. The calculator checks a² + b² ≈ c². With 3, 4, and 5: 9 + 16 = 25 → a right angle.
Do sides 3, 4, and 5 make a right angle?
Yes. 3² + 4² = 5². Scale 2 gives 6-8-10, also a right angle. At 3.05 / 4 / 5 the c gap is about 30 mm.
How does 3-4-5 differ from the slope percent calculator?
Here you check a 90° corner. A 0.6 m fall over 6 m is 10% and 5.71° — a different formula on the slope page.
Does the result replace a survey or formal hand-over?
No. It is a fast string check on site. Formal measurement needs separate equipment and documents.
Is this a free 3-4-5 ratio calculator?
Yes. Enter a, b, and c plus optional tolerance and you see whether the corner closes a right angle. No account required.
How does the 3-4-5 rule work?
The calculator checks the Pythagorean theorem: a² + b² ≈ c². With sides 3, 4, and 5 the result is a right angle (90°), because 9 + 16 = 25.
Do 6, 8, and 10 also make a right angle?
Yes. That is the 3-4-5 triple doubled. 36 + 64 = 100, so c = 10 closes the angle.
What happens at 3.05, 4, and 5?
The layout is not a perfect right triangle. Expected c ≈ 5.030 m, so the gap versus 5.0 m is about 30 mm with empty tolerance.
What is the mm tolerance for?
It compares |c − √(a²+b²)| with a millimeter limit. A wall often allows a few mm. Trim work sits nearer 1–2 mm. Empty tolerance means a strict relative compare.
What should c be when a = 3 m and b = 4 m?
Exactly 5 m. At 3 and 6 m, expected c = √(9+36) ≈ 6.708 m — that 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.
How does 3-4-5 differ from slope percent?
Here you look for a 90° corner. A 0.6 m fall over 6 m is 10% and 5.71° — a different formula on the slope page.
Do the units have to be meters?
All three sides in the same header 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).
Does the result replace a survey?
No. It is a fast string check on site. Formal construction measurement needs separate equipment.
Knowledge sources
A right angle from a² + b² = c² is the Pythagorean theorem. Units below from NIST.
Page updated October 29, 2026.