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Right Triangle Side and Angle Calculator

Free right triangle calculator — solve all sides and angles from any two known values, with area, perimeter, and formulas shown.

Enter any two values for a right triangle (right angle is always at C) — the other sides and angles solve automatically.

Side a

Side b

Hypotenuse c

Angle A (°)

Enter at least two values (any combination of sides and/or angle A) to solve the triangle.

Conventions used

Right angle is always at vertex C. Side a is opposite angle A, side b is opposite angle B, and c is the hypotenuse. A + B always equals 90°.

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Everyday Uses

Roof pitch math

Rise and run give rafter length and roof angle — essential framing calculations.

Ramp design

Compute ramp length and angle from height to meet accessibility slope limits.

Height by shadow

Measure a tree or building indirectly using distance and angle — solve the triangle.

Solving a triangle from two knowns

Solve any right triangle from two knowns, with all sides and angles shown.

Squaring a corner with 3-4-5

Measure three units along one edge and four along the other. If the diagonal is exactly five, the corner is truly square — no instrument required, and it works at any scale.

Distance from two legs of a journey

Walk three kilometres north then four east and you are five from the start. Dead reckoning and simple surveying both run on this.

Frequently Asked Questions

What information do I need to solve a right triangle?

You need any two known values among the three sides (legs a, b, and hypotenuse c) and the non-right angles (A and B), since the right angle (C = 90°) is always fixed. Two known values — whether two sides, a side and an angle, or (less commonly used here) two angles — fully determine the triangle, since trigonometric relationships and the Pythagorean theorem can derive everything else.

How do I solve for a missing angle if I know two sides?

Use inverse trigonometric functions. If you know the two legs (a, b): angle A = arctan(a/b). If you know a leg and the hypotenuse: angle A = arcsin(a/c) (using the leg opposite A) or angle A = arccos(b/c) (using the leg adjacent to A). Once you know one non-right angle, the other is simply 90° minus that angle, since all three angles of any triangle sum to 180°.

How do I find a missing side if I know one side and one angle?

Use the trigonometric ratios directly. If you know angle A and the hypotenuse c: a = c × sin(A) and b = c × cos(A). If you know angle A and leg a: b = a / tan(A) and c = a / sin(A). If you know angle A and leg b: a = b × tan(A) and c = b / cos(A). These come directly from the standard SOH-CAH-TOA relationships.

What naming convention does this calculator use for sides and angles?

The right angle is always at vertex C. Side a is opposite angle A, side b is opposite angle B, and c is the hypotenuse (opposite the right angle, and always the longest side). This is the standard convention used in most trigonometry textbooks, and angles A and B always sum to exactly 90° since C is fixed at 90° and all three angles total 180°.