Example 1 — 3 and 4
- a: 3
- b: 4
- Find c
c = 5
The most famous Pythagorean triple.
Pythagorean theorem
Know two sides of a right triangle — we find the third. Solve for the hypotenuse or either leg.
The angle between a and b must be right. Hypotenuse c is always the longest side.
Result
Choose which side to find and enter the two known lengths.
How it works
Pythagorean theorem: in a right triangle a² + b² = c², where c is opposite the right angle.
Solve for c: c = √(a² + b²). For a: a = √(c² − b²). Same idea for b.
Everyday use: screen diagonal, shortest path across a field, checking a right angle with a 3-4-5 board.
Formula
a² + b² = c²
c = √(a² + b²) ··· a = √(c² − b²) ··· b = √(c² − a²)
How to use this calculator
- Choose which side you need.
- Enter two known positive lengths.
- Read the result and the triangle sketch.
- Check that a² + b² ≈ c².
Examples
Example 2 — 5 and 12
- a: 5
- b: 12
c = 13
Another clean triple.
Example 3 — find a
- b: 8
- c: 10
a = 6
√(100 − 64) = √36 = 6.
Example 4 — find b
- a: 6
- c: 10
b = 8
The 6-8-10 triangle (double 3-4-5).
Frequently asked questions
Which side is the hypotenuse?
The longest one — opposite the right angle. If results look wrong, check you did not put a shorter side as c.
Why must c be longer than a and b?
Because c² = a² + b² is larger than either square alone. If c is shorter, you get a negative under the square root.
Only whole numbers?
No — any positive lengths work. Triples like 3-4-5 are just easy to check.
Why the sketch?
So you see which side is which. The scale follows your numbers.
Can I find a rectangle diagonal?
Yes — the sides are a and b, the diagonal is c. Same formula.
What if the triangle is not right-angled?
Pythagoras does not apply. Use the law of cosines instead.
Quick right-angle check on site?
Measure 3 and 4 on the arms; the diagonal should be 5.
Units?
Keep all sides in the same unit. The answer uses that unit too.