Enter any two known values of a right triangle — Side a, Side b, Side c (hypotenuse), or Angle A — and this calculator solves the remaining sides, angles, area, and perimeter using the Pythagorean theorem and trigonometry. Leave unknowns blank and let the calculator fill them in.
Hypotenuse (c)
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Side a
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Side b
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Angle A
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Angle B
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Area
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Perimeter
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If you know two sides, apply the Pythagorean theorem: a² + b² = c². Rearrange for the missing side — for example, if you know a and b, then c = √(a² + b²). Once all three sides are known, angles A and B follow from inverse trig: A = arcsin(a/c) and B = 90° − A.
You cannot fully solve a right triangle with only one side and no angle information — infinitely many similar triangles share the same shape. However, if you know one side and one acute angle, you can find everything else using sine, cosine, or tangent relationships (e.g. a = c × sin(A)).
Use the Pythagorean theorem when you know two sides: the missing leg is √(c² − known_leg²), and the hypotenuse is √(a² + b²). If you know one side and an angle instead, use sin, cos, or tan — for example, the side opposite angle A equals c × sin(A), and the adjacent side equals c × cos(A).
Because one angle is always 90°, the two acute angles must sum to 90°. If you know angle A, then B = 90° − A. If you know two sides, use inverse trig: A = arcsin(a/c), A = arccos(b/c), or A = arctan(a/b), depending on which sides are available.
The Pythagorean theorem states that in any right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². It only applies when one angle is exactly 90°.
A right triangle has no lines of symmetry in general, because its three sides are all different lengths. The only exception is an isosceles right triangle (45-45-90), which has exactly one line of symmetry along the altitude from the right angle to the hypotenuse.
A right triangle can have two equal sides — its two legs — making it a 45-45-90 isosceles right triangle. In that case, if both legs equal a, the hypotenuse is a√2. However, all three sides can never be equal, because an equilateral triangle has three 60° angles, not a 90° angle.
No. Two right triangles are similar only if they share the same acute angles (and therefore the same side ratios). Any pair of acute angles that sum to 90° defines a unique shape of right triangle, so there are infinitely many non-similar right triangles.