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Enter any two sides of a right triangle to instantly calculate the length of the third side.
All side lengths must be positive numbers. When solving for a leg, the hypotenuse must be greater than the known leg.
Enter known side lengths to find the unknown side.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
The Pythagorean theorem applies when one angle is 90 degrees. Let a and b be the two legs that meet at the right angle, and let c be the hypotenuse opposite it. Their squared lengths satisfy a² + b² = c². The hypotenuse is longer than either leg.
Given both legs: c = √(a² + b²)
Given the hypotenuse and one leg: missing leg = √(c² − known leg²)
The calculator offers these two solve modes. It also derives triangle area (a × b ÷ 2), perimeter (a + b + c), and the two acute angles. The result keeps the same length unit as your inputs; if the sides are in feet, the area is in square feet.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Select the hypotenuse mode when both legs are known. Select the missing-leg mode when you know the hypotenuse and one leg.
For the hypotenuse, enter a and b. For a leg, enter c first and the known leg second. Use the same unit for both values; the fields accept numeric lengths, not unit conversion.
The result updates as the values change. For example, legs 6 and 8 give c = 10, area = 24, perimeter = 24, and acute angles of about 36.87° and 53.13°. These length and area values are in the units implied by your inputs.
Check the solved side and the accompanying side, area, perimeter, and angle values. Displayed numbers are formatted to at most six decimal places.
Use cases
See how the tool fits into real work and everyday tasks.
A student who has two legs can calculate the hypotenuse, then substitute the result into a² + b² = c² to verify the relationship. The tool supplies a check; showing the intermediate squares is useful when learning the method.
A maker measuring the width and height of a rectangular panel can use those perpendicular dimensions as the legs to estimate its diagonal. Keep measurements in one unit and confirm the actual object before cutting material.
Q&A
Find concise answers to common questions and confusing cases.
Choose the missing-leg mode and enter the hypotenuse plus the other leg. The hypotenuse must be greater than the known leg so the square-root result is real and positive.
Convert both inputs to the same unit first. The calculator returns a numeric result in the input unit and does not convert measurements.
No. The equation assumes a right angle. For a triangle without a 90-degree angle, this calculation does not determine a side from the same two values.
Notes
Review scope, result limitations, and important precautions before use.
Use lengths that belong to a right triangle and identify the hypotenuse correctly. In missing-leg mode, a hypotenuse that is equal to or shorter than the known leg cannot produce a valid positive missing side. Results are rounded for display to at most six decimal places, so they may be unsuitable where a tighter measurement tolerance is required. The calculator does not account for measurement error or convert units.
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