Pythagorean Theorem Calculator
Find the hypotenuse, a missing leg, or the distance between two points — with the full step-by-step solution and exact radical form.
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Solve a right triangle
a² + b² = c² → solve for c
How It Works
The Theorem
In any right triangle, a² + b² = c², where a and b are the legs and c is the hypotenuse — the side opposite the right angle, and always the longest. It only holds for right triangles.
Finding a Leg Instead
Rearrange to b² = c² − a². The most common mistake is subtracting in the wrong order: the hypotenuse squared always comes first, because a leg is always shorter than the hypotenuse.
Exact vs Decimal Answers
Most homework wants the exact radical (5√2), not the rounded decimal (7.071). This calculator gives both, and simplifies the radical by pulling out square factors so you can match the answer key.
The Converse
Given three sides, if a² + b² = c² the triangle is right. If a² + b² > c² it is acute; if less, obtuse. That test is how "is this a right triangle?" problems are graded.
Pythagorean Triples
Whole-number side sets like 3-4-5, 5-12-13, 8-15-17, and 7-24-25 (plus every multiple: 6-8-10, 9-12-15) satisfy the theorem exactly. Recognising one lets you skip the arithmetic entirely.
The Distance Formula Is This Formula
d = √((x₂−x₁)² + (y₂−y₁)²) is the Pythagorean theorem with the horizontal and vertical gaps as legs. Same theorem, coordinate plane.
Related Tools
Already did the work? Get it checked instead.
A calculator gives you an answer. It doesn't tell you which line of your working went wrong. Photograph your own steps — handwritten notebook, whiteboard, or a screenshot of an online assignment — and Math.Photos checks them line by line, then points at the exact step where the sign flipped.
Reads handwriting
Photo of your notebook, not a retyped expression.
Step-level verdict
"Line 3 dropped a negative", not just "wrong".
Teach Me mode
Questions that lead you to the fix, not the answer.
Pricing
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