Perimeter of a Right Triangle Calculator

Enter the two legs of a right triangle to get its hypotenuse (c = √(a² + b²)), perimeter (P = a + b + c), and area (A = ½ab).

Quick Facts

Pythagorean theorem
c = √(a² + b²)
The hypotenuse c is the side opposite the right angle.
Perimeter formula
P = a + b + c
Sum of the two legs plus the hypotenuse.
Area formula
A = ½ab
The legs are perpendicular, so one serves as base and the other as height.

Your Results

Calculated
Hypotenuse (c)
-
c = √(a² + b²)
Perimeter
-
P = a + b + c
Area
-
A = ½ × a × b
Angle opposite leg a
-
arctan(a / b), in degrees

Ready

Enter the two legs and a unit, then press Calculate.

Formula and Method for the Perimeter of a Right Triangle

A right triangle has one 90° angle formed by two perpendicular sides called legs (a and b). The side opposite the right angle, called the hypotenuse (c), is always the longest side. Its length follows from the Pythagorean theorem: c = √(a² + b²). Once all three sides are known, the perimeter is simply their sum: P = a + b + c. This calculator also derives the triangle's area and one interior angle from the same two legs.

How the calculation works

Enter the lengths of the two legs and choose the unit they are measured in. The calculator first applies the Pythagorean theorem, c = √(a² + b²), to find the hypotenuse. It then adds all three sides to get the perimeter, P = a + b + c. Because the two legs are perpendicular, the area follows directly from A = ½ × a × b — no separate height measurement is needed. Finally, the angle opposite leg a is found with the inverse tangent: angle A = arctan(a / b), and the third angle is 90° minus that value (the three interior angles of any triangle sum to 180°).

Common mistakes

  • Confusing legs with the hypotenuse: the hypotenuse is always the longest side and is opposite the right angle — it can never be entered as one of the two legs.
  • Skipping the square root: a² + b² gives c², not c. Forgetting to take the square root is a common source of error when computing the hypotenuse by hand.
  • Mixing units: keep both leg lengths in the same unit — convert inches to feet, or centimeters to meters, before entering the values.

Real-world applications

  • Carpentry and construction use the 3-4-5 rule (a special case of the Pythagorean theorem) to check that corners are square before framing.
  • Fencing, edging, and trim projects use the perimeter to determine how much linear material is needed for a triangular plot or panel.
  • Roofing and ramp design use the legs and hypotenuse to compute rise, run, and slope length.
  • Surveying and navigation use right-triangle relationships to find straight-line distances from two perpendicular measurements.

Frequently Asked Questions

What is the formula for the perimeter of a right triangle?
Add all three sides: P = a + b + c, where a and b are the two legs and c is the hypotenuse. If you only know the two legs, first find the hypotenuse with the Pythagorean theorem, c = √(a² + b²), then add a + b + c.
How do I find the hypotenuse of a right triangle?
Use the Pythagorean theorem: c = √(a² + b²), where a and b are the two legs (the sides that meet at the right angle) and c is the hypotenuse (the side opposite the right angle).
How is the area of a right triangle calculated from its legs?
Since the two legs are perpendicular, one leg can serve as the base and the other as the height: A = ½ × a × b. No separate height measurement is needed.
Can I find the perimeter if I only know one leg and the hypotenuse?
Yes. Solve the Pythagorean theorem for the missing leg, b = √(c² − a²), then add all three sides: P = a + b + c.

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