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Pythagorean Calculator | Solve Right Triangles For Missing Side

Solve any right triangle with the Pythagorean theorem: find the hypotenuse from two legs, or find a missing leg from the hypotenuse and one leg. The squared steps are shown, and the tool also confirms whether three side lengths form a right triangle — a staple for construction and geometry.

Last updated: June 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

Pythagorean tripleCheck
3, 4, 59 + 16 = 25
5, 12, 1325 + 144 = 169
8, 15, 1764 + 225 = 289
7, 24, 2549 + 576 = 625

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

school Free for classroom use

Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

Solving for…Rearranged formula
Hypotenuse cc = √(a² + b²)
Leg aa = √(c² - b²)
Leg bb = √(c² - a²)

lightbulb Worked example

Let's say you are using the Pythagorean Theorem Calculator. Solves right-triangle problems using the Pythagorean theorem. Enter the lengths of any two sides — the two legs or one leg and the hypotenuse — and the tool computes the missing side using a² + b² = Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula a² + b² = c² (a and b are legs, c is the hypotenuse) and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: a² + b² = c² (a and b are legs, c is the hypotenuse)

The Pythagorean Theorem Calculator is built on a well-established calculation method. It uses the formula a² + b² = c² (a and b are legs, c is the hypotenuse) to turn your inputs into a reliable result. Solves right-triangle problems using the Pythagorean theorem. Enter the lengths of any two sides — the two legs or one leg and the hypotenuse — and the tool computes the missing side using a² + b² = c², with the working The steps are shown on the page so you can follow the reasoning from input to output.

How the Pythagorean theorem works

In any right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides.

Example: legs 6 and 8

c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Finding a leg

If c = 13 and one leg b = 5, then a = √(13² - 5²) = √(169 - 25) = √144 = 12 (the 5-12-13 triple).

The theorem only applies to right triangles. Whole-number side sets like 3-4-5 are called Pythagorean triples.

What is the Pythagorean Theorem Calculator?

The Pythagorean Theorem Calculator is a free, browser-based math calculator tool that helps you Solves right-triangle problems using the Pythagorean theorem. Enter the lengths of any two sides — the two legs or one leg and the hypotenuse — and the tool com. Instead of working through the math by hand or in a spreadsheet, you enter your values and the calculator returns an accurate result instantly — while still showing the formula and the steps so you can verify the reasoning. It is designed for quick everyday use: no sign-up, no installation, and everything runs locally in your browser for complete privacy.

How to use the Pythagorean Theorem Calculator

  1. Enter the required values into the input fields.
  2. Press the calculate button — the result appears immediately, updated live as you change any value.
  3. Read the step-by-step breakdown below the result to see exactly how the calculation was performed.
  4. Use the interpretation guide to understand what the result means for your situation, and try different inputs to see how they change the outcome.

How to use the Pythagorean Calculator

Enter the lengths of any two sides of a right triangle — the two legs, or one leg and the hypotenuse — and press calculate. The tool solves for the missing side using a² + b² = c², where c is always the hypotenuse, the side opposite the right angle. For a 3-4-5 triangle, entering 3 and 4 returns 5; entering 5 and 4 returns 3 for the other leg. You can also use it in reverse to check whether a triangle is right-angled by testing whether the sides satisfy the theorem.

Interpreting your result

The result is the exact length of the missing side in the same units you entered, plus the area and perimeter where applicable. In real life this is the measurement you can't take directly: the diagonal of a TV, the height of a ladder needed to reach a window, or the straight-line distance across a rectangular field. The calculator also identifies the Pythagorean triple pattern (like 6-8-10) when the sides are whole numbers, which is useful for construction layout and checking squareness.

Common mistakes to avoid

The most common error is putting the hypotenuse in the wrong place — c must be the side opposite the right angle, never one of the legs. Second, forgetting to take the square root: a² + b² gives c², not c. Third, mixing units — convert feet and inches to a single unit before calculating. Finally, applying the theorem to non-right triangles: for other triangles you need the law of cosines, and the calculator will flag when the entered sides cannot form a right triangle.

Tips for best results

Use the calculator when laying out foundations or fences: a 3-4-5 check (measuring 3 ft on one side, 4 ft on the other, adjusting until the diagonal is 5 ft) guarantees a square corner. For staircases and ramps, the theorem gives the exact stringer length you need before cutting. Remember that the theorem works in any unit system — the result carries the same unit as the input. When checking a real triangle, always verify the largest side is the candidate hypotenuse before testing.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c², where c is the hypotenuse (the side opposite the 90-degree angle) and a and b are the legs. It lets you find any one side when the other two are known.
How do you find the hypotenuse?
The hypotenuse is the side opposite the right angle, and you find it with a² + b² = c², where c is the hypotenuse. Square both known legs, add them, and take the square root. For a right triangle with legs 3 and 4, c = √(9 + 16) = √25 = 5. The calculator accepts any two sides and solves for the third.
How do you find a missing leg?
Rearrange the formula to subtract instead of add: a = √(c² - b²). If the hypotenuse is 13 and one leg is 5, the other leg is √(169 - 25) = √144 = 12. Make sure you subtract the known leg's square from the hypotenuse's square, not the other way around.
What is a Pythagorean triple?
A Pythagorean triple is a set of three whole numbers that satisfy a² + b² = c², such as 3-4-5, 5-12-13, and 8-15-17. Any multiple of a triple is also a triple (6-8-10, for example). Recognizing them lets you solve right triangles instantly without a calculator.
Does the Pythagorean theorem work for all triangles?
No, only for right triangles — those with a 90-degree angle. For non-right triangles you need the law of cosines, c² = a² + b² - 2ab cos(C), which reduces to the Pythagorean theorem when angle C is 90 degrees (because cos 90 = 0).
What does the Pythagorean Theorem Calculator do?
Solves right-triangle problems using the Pythagorean theorem. Enter the lengths of any two sides — the two legs or one leg and the hypotenuse — and the tool computes the missing side using a² + b² = c², with the working shown. It also lists common Pythagorean. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Pythagorean Theorem Calculator use?
The Pythagorean Theorem Calculator applies the standard formula: a² + b² = c² (a and b are legs, c is the hypotenuse). The tool walks through each step of the calculation so you can verify the numbers yourself.
Is the Pythagorean Theorem Calculator free and private?
Yes — the Pythagorean Theorem Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Pythagorean Theorem Calculator?
The Pythagorean Theorem Calculator applies the standard formula: a² + b² = c² (a and b are legs, c is the hypotenuse). It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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