Enter any two positive sides of a right triangle to find the third. The tool uses c² = a² + b² where c is the hypotenuse (longest side). Works whether you measure in inches, feet, centimetres, or metres — keep units consistent in your own working.
One leg next to the right angle. Leave empty if this is what you want to find.
The other leg. Leave empty if this is what you want to find.
Longest side, opposite the right angle. Leave empty if you want to find it from two legs.
Enter any two positive sides of a right triangle to find the third. The tool uses c² = a² + b² where c is the hypotenuse (longest side). Works whether you measure in inches, feet, centimetres, or metres — keep units consistent in your own working.
For legs a and b and hypotenuse c: c² = a² + b² If both legs are known: c = √(a² + b²) If the hypotenuse c and one leg are known: other leg = √(c² − known_leg²)
If a = 3 and b = 4, then c = √(9 + 16) = √25 = 5. If instead c = 13 and a = 5, the other leg is √(169 − 25) = √144 = 12.
It is the side opposite the right angle and is always the longest side. If you label the two shorter sides as legs, the hypotenuse is the remaining side.
Not inside one run of the formula — convert so every side uses the same unit first. The calculator only does the Pythagorean relationship on the numbers you enter.
This tool only applies to right triangles (90° corners). For other triangles you would use different rules such as trigonometry or the cosine rule.
Yes, if the situation forms a right triangle (for example vertical height and horizontal distance along the ground). Model the two perpendicular distances as legs and interpret the result as the sloping length.
Students in the US and UK bump into the Pythagorean theorem whenever right triangles appear in geometry, construction sketches, and applied problems. This article strips the idea down to one dependable relationship between the two legs and the hypotenuse, then shows how to turn two known sides into the missing length — without mixing units.
Label the two sides that meet at the right angle as legs a and b, and label the longest side (opposite the right angle) as c. The theorem states c² = a² + b². If you know both legs, add their squares and take the square root to read off the hypotenuse. If you know the hypotenuse and one leg, subtract the known square from c² and take the square root to recover the other leg. The same algebra appears whether you work in feet, inches, metres, or centimetres; only the unit labels change.
c² = a² + b²; c = √(a² + b²); a = √(c² − b²); b = √(c² − a²) for positive lengths with c greater than each leg when all three are known.
Picture a rectangular corner on a floor plan with legs 6 ft and 8 ft along the walls. The diagonal shortcut across the corner has length √(36 + 64) = 10 ft. In metric, legs 2.5 m and 6.0 m give hypotenuse √(6.25 + 36) ≈ 6.5 m. If you know a 5.0 m hypotenuse along that diagonal and one leg is 3.0 m, the other leg is √(25 − 9) = 4.0 m.
Open the tool page and type any two positive side lengths in the leg a, leg b, and hypotenuse boxes, leaving exactly one box empty for the value you want. Press calculate to see the relationship used, the numeric result, and a quick consistency check. If you ask for a leg from a hypotenuse, make sure the hypotenuse is larger than the leg you already entered — otherwise the triangle cannot close.
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