Triangle Calculator
This free right triangle calculator solves for a missing side using the Pythagorean theorem, or for every side and angle from one known angle and one known side. It also computes area and perimeter. Nothing you enter is sent anywhere or stored.
How to Use It
- Find a Side: enter any two of the three sides (Leg a, Leg b, Hypotenuse c) and leave the third blank.
- Find Sides from a Side and an Angle: enter a known angle, a known side length, and which side it is relative to the angle.
- Both panels update instantly as you change any field.
How It Works
The Pythagorean theorem, a² + b² = c², relates the two legs of a right triangle to its hypotenuse. Given any two of the three sides, the third follows directly: add the squares of both legs and take the square root for the hypotenuse, or subtract the known leg's square from the hypotenuse's square and take the square root for the other leg. From there, both non-right angles follow from the inverse sine of a leg divided by the hypotenuse.
Formulas
a² + b² = c²
sin(angle) = opposite ÷ hypotenuse
cos(angle) = adjacent ÷ hypotenuse
tan(angle) = opposite ÷ adjacent
The second panel works from basic trigonometric ratios instead: given one acute angle and one side, the other two sides follow from sine, cosine, and tangent, depending on whether the known side is opposite the angle, adjacent to it, or the hypotenuse.
A worked example, the classic 3-4-5 right triangle: legs of 3 and 4 give a hypotenuse of exactly 5, angles of about 36.87° and 53.13°, an area of 6, and a perimeter of 12. Everything runs client-side in your browser. Nothing you enter is sent anywhere or stored.
Frequently Asked Questions
What is the Pythagorean theorem?
For any right triangle, the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². The "Find a Side" panel above uses this to solve for whichever side you leave blank, given the other two.
Does this tool solve triangles that are not right triangles?
No, this tool is deliberately scoped to right triangles. General triangle solving from an arbitrary combination of known sides and angles has real edge cases, most notably the ambiguous case where two sides and a non-included angle can describe zero, one, or two different valid triangles, which is a meaningfully different and more complex problem than what most "Pythagorean theorem" or "right triangle" searches are actually asking for.
How does the "This side is" dropdown work in the second panel?
It tells the tool how your known side relates to your known angle. "Opposite the angle" means the side directly across from it, "Adjacent to the angle" means the side next to it (not the hypotenuse), and "The hypotenuse" is always the longest side, opposite the right angle. Picking the correct option is what lets the tool apply the right trigonometric ratio.
Why does entering all three sides in the first panel produce an error instead of a result?
If all three sides are entered, one of them might not actually be consistent with the Pythagorean theorem applied to the other two. Rather than silently picking two of the three and ignoring what you typed into the third, the tool asks you to leave one field blank so it's always clear which two values it solved from.
What units does this tool use?
None specifically, the side lengths and results are unitless numbers. Enter your measurements in whatever unit you're working in (inches, feet, meters, anything consistent), and the results come back in that same unit.