Pythagorean Theorem Calculator
Pick which side of the right triangle is unknown, enter the two known sides, and see the missing side worked out step by step.
c = 5
Hypotenuse of the right triangle
c² = a² + b²
c = √(3² + 4²)
c = √(9 + 16) = √25
c = 5
Area: 6
Perimeter: 12
Pythagorean triples
A Pythagorean triple is a right triangle whose three sides are all whole numbers. The best known is 3-4-5, used on building sites to check that a corner is square — and every multiple of it, such as 6-8-10 or 9-12-15, is also a triple.
- 3² + 4² = 5² (9 + 16 = 25)
- 5² + 12² = 13² (25 + 144 = 169)
- 8² + 15² = 17² (64 + 225 = 289)
- 7² + 24² = 25² (49 + 576 = 625)
- 20² + 21² = 29² (400 + 441 = 841)
Calculated on your device — nothing is sent anywhere.
How it works
- Choose which side is unknown — leg a, leg b, or the hypotenuse c.
- Type the lengths of the two known sides; any unit works as long as both use the same one.
- Read the missing side with the substituted formula, plus the triangle’s area, perimeter, and a scaled drawing.
Frequently asked questions
- What is the Pythagorean theorem formula?
- For a right triangle with legs a and b and hypotenuse c, the theorem states a² + b² = c². The hypotenuse is the side opposite the 90° angle and is always the longest side. Rearranging gives c = √(a² + b²) for the hypotenuse and a = √(c² − b²) for a missing leg.
- How do I find a leg when I know the hypotenuse?
- Subtract the square of the known leg from the square of the hypotenuse, then take the square root: a = √(c² − b²). The hypotenuse must be longer than the known leg — if it is not, no right triangle exists with those measurements, and the calculator will tell you so.
- What units does the calculator use?
- The theorem is unit-agnostic, so you can enter centimeters, meters, inches, feet, or anything else — the answer comes out in the same unit. The only rule is that both known sides must use the same unit. Area is then in that unit squared and perimeter in the same linear unit.
- What are Pythagorean triples like 3-4-5 used for?
- A Pythagorean triple is a set of three whole numbers that satisfy a² + b² = c², such as 3-4-5 or 5-12-13. Builders and carpenters use the 3-4-5 rule to check that a corner is square: measure 3 units along one edge, 4 along the other, and the diagonal should be exactly 5. Any multiple, like 6-8-10 or 9-12-15, works the same way.
- Are my numbers sent to a server?
- No. Every calculation and the triangle drawing run entirely in your browser with no network requests, so nothing you type is uploaded or stored. The page keeps working offline once loaded, which makes it usable on a job site or in a classroom with poor connectivity.
About this tool
This calculator solves the Pythagorean theorem for any side of a right triangle. Choose whether leg a, leg b, or the hypotenuse c is the unknown, enter the other two sides, and the missing length appears instantly — together with the formula substituted step by step, so you can see exactly how the answer was reached rather than just what it is. The area and perimeter of the triangle are computed at the same time, and a small drawing renders the triangle to scale with the right angle marked, which makes obviously wrong inputs easy to spot at a glance.
The math follows the theorem directly: a² + b² = c². Solving for the hypotenuse squares both legs, adds them, and takes the square root; solving for a leg subtracts the known leg’s square from the hypotenuse’s square first. The calculator validates that the hypotenuse is longer than the known leg — a triangle where it is not cannot exist — and reports the result to four decimal places. Everything runs client-side in JavaScript with no network requests, so your figures never leave the device.
Typical uses are broader than homework. Carpenters and DIY builders use the theorem to square up decking, framing, and foundations with the 3-4-5 rule; the details section lists the common whole-number triples for exactly that purpose. It also answers everyday sizing questions: the diagonal of a TV or monitor from its width and height, the length of ladder needed to reach a given height at a safe distance from the wall, or the straight-line distance across a rectangular field.
Two practical tips. First, the step-by-step working shown under the result matches the layout teachers expect, so students can copy it as a model for showing their own work. Second, if your two known sides form a ratio close to a listed triple, the exact triple is often the intended answer — measurement error, not math, usually explains the difference.