Right Triangle Calculator
Calculate sides, angles, area, and perimeter of right triangles.
A right triangle calculator solves for missing sides, angles, area, and perimeter of a right triangle given two known measurements.
Examples
3-4-5 triangle
Angle and side
45-45-90
Frequently Asked Questions
What are SOH-CAH-TOA?
What is the inradius?
What is the circumradius?
Quick Tips
- •Double-check your inputs — small errors lead to incorrect results.
- •Remember to convert degrees to radians if your formula requires it.
- •Use SOH-CAH-TOA to verify trigonometric results independently.
A right triangle calculator solves for missing sides, angles, area, and perimeter of a right triangle given two known measurements.
How to Use This Calculator
Choose between entering two sides or one side plus one angle. The calculator will solve for all unknown sides and angles of the right triangle, plus compute area, perimeter, and radii.
Understanding the Formula
a² + b² = c²; sin(A) = a/c; cos(A) = b/c; tan(A) = a/b; Area = (a × b)/2
Examples
3-4-5 triangle
a=3, b=4: c=5, A≈36.87°, B≈53.13°, Area=6
Angle and side
Angle 30°, hypotenuse 10: a=5, b=8.66
45-45-90
a=1, b=1: c=√2≈1.414, angles are both 45°
Frequently Asked Questions
What are SOH-CAH-TOA?
Memory aids for trig ratios: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.
What is the inradius?
The inradius is the radius of the largest circle that fits inside the triangle. For a right triangle: r = (a + b - c) / 2.
What is the circumradius?
The circumradius is the radius of the circle that passes through all three vertices. For a right triangle: R = c / 2 (half the hypotenuse).
Assumptions & Limitations
- Assumes Euclidean geometry and a valid right triangle with one 90-degree angle.
- Assumes exact input values; rounding in inputs propagates to results.
- Results may show floating-point approximations for irrational numbers.