Right Triangle Calculator

About the Right Triangle Calculator

A right triangle calculator solves for all unknown sides and angles of a right triangle from any two known values — using the Pythagorean theorem for sides and basic trigonometry (SOH-CAH-TOA) for angle calculations. The right triangle is the foundational geometric shape of trigonometry and appears throughout engineering, navigation, surveying, architecture, physics, and daily problem-solving. Whether you need to find the length of a ladder resting against a wall, calculate the slope of a ramp, determine the distance across a body of water using a known angle and baseline, or verify that a corner is perfectly square (the 3-4-5 check), right triangle calculations are the tool. Our calculator accepts any two values from the four quantities: the two legs (sides a and b adjacent to the right angle), the hypotenuse (side c), or angle A (opposite to side a). From any two values, it solves for all remaining quantities and also provides the area and perimeter. The Pythagorean theorem (c² = a² + b²) and the trigonometric functions (sin A = a/c, cos A = b/c, tan A = a/b) govern all calculations. Results are shown to 4 decimal places for precision engineering work.

How It Works

Given legs a and b: c = √(a² + b²) (Pythagorean theorem). Angle A = arctan(a/b) degrees. Angle B = 90° − A. Given a and hypotenuse c: b = √(c² − a²). Angle A = arcsin(a/c). Given b and c: a = √(c² − b²). Angle A = acos(b/c). Given leg a and angle A: c = a / sin(A). b = √(c² − a²) = a × cos(A) / sin(A) = a / tan(A). Area = ½ × a × b. Perimeter = a + b + c. Example: a = 3, b = 4. c = √(9+16) = 5. Angle A = arctan(3/4) = 36.87°. Angle B = 53.13°. Area = ½ × 3 × 4 = 6. Perimeter = 12. Pythagorean triples (integer solutions): (3,4,5); (5,12,13); (8,15,17); (7,24,25); (9,40,41). A (6,8,10) triple is just (3,4,5) scaled by 2.

Tips & Best Practices

• ✓The 3-4-5 rule for square corners: in construction, a right angle can be verified by measuring 3 units along one wall, 4 units along the adjacent wall, and checking the diagonal is exactly 5 units. This works in any consistent units. Any multiple (6-8-10, 9-12-15, etc.) works equally well.
• ✓Slope and grade: in road engineering and construction, slope is expressed as rise/run (the same as tan(angle)). A 5% grade means tan(angle) = 0.05, so angle = arctan(0.05) = 2.86°. The right triangle calculation converts between grade percentage, angle, rise, and run.
• ✓Surveying with angles: given a baseline distance and an angle to a landmark, the distance to the landmark is: hypotenuse = baseline / cos(angle) if the baseline is the adjacent side, or baseline / sin(angle) if it is the opposite side. This is the basic principle of triangulation.

Who Uses This Calculator

Students solving trigonometry and geometry homework problems. Construction workers and carpenters checking for square corners and calculating roof pitches and rafter lengths. Engineers calculating force components, beam geometry, and structural diagonals. Surveyors and navigators solving distance and angle problems. DIY enthusiasts calculating stair rise/run, ramp angles, and ladder lengths.