Pythagorean Theorem Calculator
Find any missing side of a right triangle using a² + b² = c².
About Pythagorean Theorem Calculator
The Pythagorean theorem states that in any right triangle the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². To find the hypotenuse, add the squares of the legs and take the square root. To find a missing leg, subtract the square of the known leg from the square of the hypotenuse and take the square root. Famous integer solutions (Pythagorean triples) include 3-4-5, 5-12-13, 8-15-17 and 7-24-25.
Formulas
Pythagorean theorem
a² + b² = c²
- a
- Leg a
- b
- Leg b
- c
- Hypotenuse (longest side)
Solve for hypotenuse
c = √(a² + b²)
Solve for a leg
a = √(c² − b²)
Worked example
With the default values below, Pythagorean Theorem Calculator returns Missing side of 5.00000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Solve forone of Hypotenuse c (given a and b), Leg a (given b and c), Leg b (given a and c)
- Hypotenuse c (given a and b)
- Leg aminimum 0
- 3
- Leg bminimum 0
- 4
- Hypotenuse cminimum 0
- 5
Results
- Missing side
- 5.00000000
- Leg a
- 3.00000000
- Leg b
- 4.00000000
- Hypotenuse c
- 5.00000000
- Verification
- 3² + 4² = 5² → 9 + 16 = 25
Step by step
- 1Write the theorem
- 2Substitute
- 3Solve for Hypotenuse c= 5
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What are Pythagorean triples?
A Pythagorean triple is a set of three positive integers (a, b, c) where a² + b² = c². The most famous is 3-4-5 (9 + 16 = 25). Others include 5-12-13, 8-15-17, and any multiple of these, like 6-8-10.
Does the theorem work in 3D?
Yes. The 3D diagonal d of a box with dimensions a, b, c is d = √(a² + b² + c²), which applies the Pythagorean theorem twice — once for the floor diagonal, then again for the space diagonal.
Why does the hypotenuse have to be the longest side?
The right angle is the largest angle in a right triangle. In any triangle, the longest side is opposite the largest angle. So the side opposite 90° (the hypotenuse) is always the longest.