Triangle Calculator
Quickly find your Triangle measurements with our free Triangle Calculator. Simple, fast, and accurate.
Right-triangle legs
Result
What is a Triangle Calculator?
A triangle calculator solves for the missing side, area, perimeter, and angles of a right triangle given two legs. It uses the Pythagorean theorem and trigonometric functions to return complete triangle measurements.
How to calculate triangle measurements manually (the formula)
For a right triangle with legs a and b: Hypotenuse c = √(a2 + b2). Area = ½ab. Perimeter = a + b + c. Angle α = arctan(a/b), β = 90° − α.
Example calculation
Legs 3 and 4: Hypotenuse = √(9 + 16) = 5. Area = ½ × 3 × 4 = 6. Perimeter = 3 + 4 + 5 = 12. Angles: about 36.87° and 53.13°.
Common mistakes
- Applying right-triangle formulas to non-right triangles — The Pythagorean theorem and simple trigonometric ratios only work for right triangles.
- Forgetting units — All sides must be in the same unit. Area will be in square units, perimeter in linear units.
- Confusing opposite and adjacent sides — For angle calculations, identify which leg is opposite and which is adjacent to the angle in question.
Frequently asked questions
What is a right triangle?
A right triangle has one 90\u00b0 angle. The side opposite the right angle is the hypotenuse, and the other two sides are the legs.
How do you find the hypotenuse?
Use the Pythagorean theorem: c = \u221a(a\u00b2 + b\u00b2), where a and b are the legs.
How do you calculate the area of a right triangle?
Multiply the legs and divide by 2: A = \u00bdab. The legs are perpendicular, so they serve as base and height.
How do you find the perimeter of a right triangle?
Add all three sides: P = a + b + c. First find the hypotenuse using the Pythagorean theorem if needed.
How do you find the angles of a right triangle?
Use inverse tangent: \u03b1 = arctan(a/b) and \u03b2 = 90\u00b0 - \u03b1. The right angle is always 90\u00b0.
Can you use the Pythagorean theorem for any triangle?
No. The Pythagorean theorem only works for right triangles. For other triangles, use the law of cosines.