Enter any two known values of a right triangle — such as side a, side b, side c (hypotenuse), angle α, or angle β — and this calculator solves the remaining unknowns. You'll get all three sides, both acute angles, the area, and the perimeter of your right triangle instantly. Also try the calculate Cosine (cos) cos(x).
Side c (Hypotenuse)
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Side a
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Side b
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Angle α
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Angle β
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Area
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Perimeter
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Apply the Pythagorean theorem: a² + b² = c². If you know sides a and b, the hypotenuse is c = √(a² + b²). If you know one leg and the hypotenuse, find the missing leg with a = √(c² − b²) or b = √(c² − a²). Once all sides are known, use inverse trig functions (arctan, arcsin, arccos) to find the angles.
If you know two sides, use inverse trigonometric functions. For example, angle α = arctan(a / b), or α = arcsin(a / c), or α = arccos(b / c). Remember that in any right triangle, the two acute angles always sum to 90°, so once you find one, subtract it from 90° to get the other.
With only one side, you need at least one angle as well. Given one side and one acute angle, you can find every other part of the triangle using sine, cosine, and tangent ratios. For example, if you know side a and angle α, then b = a / tan(α) and c = a / sin(α).
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². It applies to every right triangle regardless of the angle sizes, and is one of the most fundamental formulas in geometry and trigonometry.
A standard right triangle (with two unequal acute angles) has zero lines of symmetry. The only exception is an isosceles right triangle (45°–45°–90°), which has exactly one line of symmetry running from the right-angle vertex to the midpoint of the hypotenuse.
Yes — a 45°–45°–90° triangle has two equal legs (sides a and b are equal). In this special case the hypotenuse is exactly a√2. Any other right triangle will have all three sides of different lengths.
No. Right triangles are only similar if they share the same acute angle measures. Two right triangles that both have a 30°–60°–90° layout are similar, but a 30°–60°–90° triangle and a 45°–45°–90° triangle are not similar because their angle pairs differ.
Degrees and radians are two units for measuring angles. A full circle is 360° or 2π radians. To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π. This calculator supports both units — select your preferred unit before entering angle values.