HesapHanem

Right Triangle Side Calculator

Solve the missing side of a right triangle in seconds.

How it is calculated

For a right triangle with legs a and b and hypotenuse c, the tool rearranges a² + b² = c² to b = √(c² − a²) and then finds the area as area = a × b ÷ 2. Enter the leg you know and the hypotenuse, the longest side opposite the right angle, in the same length unit; the answer is in that unit and the area in its square. The hypotenuse must be strictly greater than the leg and the leg greater than zero. Otherwise no result is shown, since no right triangle exists with a hypotenuse equal to or shorter than a leg. Both results are rounded to two decimals, so a very small leg can show as 0.00.

Worked example

A ladder leans against a wall: the ladder is 13 long (the hypotenuse) and the foot is 7 from the wall (a known leg). Squares: 13² = 169 and 7² = 49. Difference: 169 − 49 = 120. Square root: √120 = 10.954, shown as 10.95, which is how high the ladder reaches. Area: 7 × 10.954 ÷ 2 = 38.34, in square units of the same length unit.

Try this example →

Common mistakes

  • Typing the longest side into the Known leg box and a shorter side into the Hypotenuse box. The hypotenuse must be the larger number, and the tool returns no result if it is not.
  • Entering a slanted side that is not the hypotenuse, for example a rafter length measured along the roof as if it were a leg. The hypotenuse is always opposite the right angle.
  • Mixing units, such as one side in centimetres and the other in metres. Convert both to the same unit first.
  • Applying this to a triangle that has no right angle. For any other triangle the Pythagorean relation does not hold and the answer is wrong.
  • Reading the area as a length. It is in square units, so 38.34 means square metres if the sides were in metres.

About this calculator

The Pythagorean theorem, a² + b² = c², relates the two legs of a right triangle to its hypotenuse, and rearranging it lets you solve for whichever side is missing given the other two — if you know one leg and the hypotenuse, the missing leg is √(c² − a²). Once all three sides are known, the triangle’s area follows immediately as half the product of the two legs.

This is one of the most-used formulas in practical trades: carpenters and framers use it to confirm a corner is square (the classic 3-4-5 rule is just a Pythagorean triple), roofers use it to find rafter lengths from rise and run, and surveyors and navigators use it to compute straight-line distances from two perpendicular offsets. It’s equally foundational in physics for resolving vector components and in construction and CAD software for validating right-angle geometry before cutting material.

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