Missing Side of a Right Triangle Calculator

Enter any two of a right triangle's three sides — the two legs, or one leg and the hypotenuse — and leave the unknown one blank to solve it with the Pythagorean theorem, a² + b² = c².

Quick Facts

Pythagorean theorem
a² + b² = c²
Legs a and b form the right angle; c is the hypotenuse.
Hypotenuse rule
c is always the longest side
It sits opposite the 90° angle.
Common integer triples
3-4-5, 5-12-13, 8-15-17
Whole-number right triangles worth memorizing.

Your Results

Calculated
Side a (leg)
-
Leg forming the right angle
Side b (leg)
-
Leg forming the right angle
Hypotenuse c
-
Longest side, opposite the right angle
Triangle Area
-
Area = ½ × a × b

Ready

Enter any two of the three side lengths and leave the third blank, then press Calculate.

Formula and Method for the Missing Side of a Right Triangle

A right triangle has one 90° angle. The two shorter sides that form that angle are called the legs (a and b), and the side opposite the right angle — always the longest side — is the hypotenuse (c). The Pythagorean theorem ties them together: a² + b² = c². Given any two of the three sides, this calculator solves for the missing one and also reports the triangle's perimeter and area.

How the calculation works

Enter two of the three side lengths and leave the unknown one blank. If the hypotenuse is missing, the calculator adds the squares of the two legs and takes the square root: c = √(a² + b²). If a leg is missing, it rearranges the theorem instead: a = √(c² − b²), or b = √(c² − a²). Because a leg must be shorter than the hypotenuse, the hypotenuse you enter always has to be larger than the known leg — otherwise the value under the square root would be negative, which isn't a real length. If you enter all three sides, the calculator checks that a² + b² = c² holds before reporting the perimeter and area, so you can confirm the triangle really has a right angle.

Common mistakes

  • Mixing up the hypotenuse: the hypotenuse is always the longest side and always sits opposite the 90° angle — never enter it into the "Side a" or "Side b" leg fields.
  • Subtracting the wrong way: when solving for a leg, you subtract the known leg's square from the hypotenuse's square (c² − b²), not the other way around — the hypotenuse is always larger.
  • Mixing units: keep every side length in the same unit (all feet, all meters, etc.) before entering values; convert first if your measurements come in different units.

Real-world applications

  • Construction and carpentry use the 3-4-5 rule (or this calculator) to square up corners, framing, and foundations.
  • Roofing and ramp design use leg-and-hypotenuse relationships to size rafters, braces, and slope lengths.
  • Navigation and surveying use right-triangle side relationships to find straight-line distances between two perpendicular offsets.
  • Ladder and safety placement rely on the same math to check that a ladder's length, wall height, and base distance are consistent.

Frequently Asked Questions

How do I find a missing side of a right triangle?
Use the Pythagorean theorem, a² + b² = c², where c is the hypotenuse and a and b are the two legs. If the hypotenuse is missing, c = √(a² + b²). If a leg is missing, solve for it as a = √(c² − b²) or b = √(c² − a²).
Which side of a right triangle is the hypotenuse?
The hypotenuse is the side directly opposite the right angle (90°), and it is always the longest of the three sides. The other two sides, called legs, form the right angle itself.
What if I only know one side and an angle, not two sides?
The Pythagorean theorem needs two known sides. If you only have one side and one angle, use trigonometric ratios instead: sin(angle) = opposite/hypotenuse, cos(angle) = adjacent/hypotenuse, and tan(angle) = opposite/adjacent.
Can any three side lengths form a right triangle?
No. Three lengths only form a right triangle if the square of the longest side equals the sum of the squares of the other two, a² + b² = c². This calculator checks that relationship whenever you enter all three sides.

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