How this calculation works
The two entered sides must meet at a right angle. This formula does not apply to an arbitrary pair of sides in a non-right triangle.
Hypotenuse = √(a² + b²)A worked example
A right triangle with perpendicular sides 3 and 4 has a hypotenuse of 5.
Good to know
Uses the stated formula and assumptions. Displayed decimal values are rounded; use consistent units for all inputs.
The 3–4–5 example is a useful right-angle check
The squares 3² and 4² add to 25, the square of 5. Scaling all three lengths by the same factor preserves that equality, so 6–8–10 and 9–12–15 describe the same right-triangle proportions.
The relationship is about squared lengths, not the sum of ordinary lengths. A side of 3 plus a side of 4 traces a bent route of 7; the straight hypotenuse is 5.
The entered sides must meet at a right angle
The formula does not determine the third side of an arbitrary triangle from just two sides. Without a right angle, the angle between the sides changes the third side. Make sure your measurement or problem supplies the required geometry.
Use the same units for both sides. Converting 300 cm to 3 m before pairing it with 4 m gives a 5 m hypotenuse; entering 300 and 4 without conversion answers a different problem.
A few questions, answered
Is the hypotenuse the longest side?
Yes, for a non-degenerate right triangle it is longer than either perpendicular side.
Can I use this for a rectangle’s diagonal?
Yes. The length and width of a rectangle are perpendicular sides of the relevant right triangle.