What is a triangle calculator?
A triangle calculator computes the area, perimeter, and height of a triangle from the dimensions you provide. You can enter either three sides (SSS: side-side-side) or two sides and the included angle (SAS: side-angle-side). The calculator uses Heron's formula for area when three sides are given, and trigonometry when two sides and an angle are given. It is useful for geometry homework, construction, design, and any situation where you need triangle measurements.
This free triangle calculator runs in your browser. Enter the side lengths (and optionally one angle for SAS), and the tool displays the area in square units, the perimeter in units, and the height from side A. No sign-up or download is required. Use it for right triangles, equilateral triangles, or any scalene triangle as long as the sides satisfy the triangle inequality.
How to use this triangle calculator
For SSS (three sides): Enter the length of side A, side B, and side C. All three must be positive, and the sum of any two sides must be greater than the third side. The calculator then computes the area using Heron's formula, the perimeter as the sum of the three sides, and the height from side A. For SAS (two sides and included angle): Enter side A, side B, and angle C in degrees. Angle C is the angle between sides A and B. The calculator finds side C using the law of cosines, then computes area as half the product of two sides and the sine of the included angle, and the perimeter and height from that.
The inputs are grouped into Sides and Angles. Leave angles blank when using three sides. When using SAS, enter only the two sides and the included angle (angle C). Results appear in the result box on the right. If the sides do not form a valid triangle, a message explains what to check.
Triangle area formulas
When you have three sides (SSS), the area is calculated with Heron's formula. First find the semi-perimeter s = (a + b + c) / 2. Then area = √(s(s − a)(s − b)(s − c)). This works for any triangle. When you have two sides and the included angle (SAS), area = (1/2) × a × b × sin(C), where C is the angle between sides a and b. The calculator uses these formulas automatically, so you get accurate area, perimeter, and height without doing the math by hand.
Perimeter and height
The perimeter of a triangle is the sum of its three side lengths: P = a + b + c. For SAS, the third side is found with the law of cosines: c² = a² + b² − 2ab cos(C). The height from side A is the perpendicular distance from the vertex opposite A to side A. It is related to the area by height = 2 × area / a. This calculator gives the height from side A; you can use the same formula with b or c if you need height from another side.
Triangle inequality
Three positive numbers can be the sides of a triangle only if the sum of any two is greater than the third. That is, a + b > c, b + c > a, and a + c > b. If you enter sides that do not satisfy this, the calculator cannot form a triangle and will not show area or perimeter. Check your inputs and adjust so that each side is less than the sum of the other two. For example, 3, 4, 5 is a valid right triangle; 1, 2, 10 is not valid because 1 + 2 is not greater than 10.
Right triangles and special cases
A right triangle has one 90° angle. If you enter sides 3, 4, and 5, you get a right triangle (3² + 4² = 5²). The area is 6 square units and the perimeter is 12 units. An equilateral triangle has three equal sides; enter the same value for A, B, and C to get area and perimeter for an equilateral triangle. For SAS, the included angle C must be between 0° and 180°. Enter sides and angle in the Sides and Angles sections as described above.
Applications of triangle calculations
Triangle area and perimeter are used in construction (roofs, trusses), land surveying, graphics and design, physics (forces, vectors), and education. Knowing how to compute area from sides or from two sides and an angle is a fundamental geometry skill. This calculator helps you check homework, prepare materials lists, or quickly get measurements without manual formula work. For real-world use, ensure your units are consistent (e.g. all sides in meters or all in feet).
Summary
This triangle calculator finds the area, perimeter, and height of a triangle from three sides (SSS) or two sides and the included angle (SAS). Enter values in the Sides and Angles sections; for SSS leave angles blank. Results appear in the result box. The tool uses Heron's formula for SSS and trigonometry for SAS. It is free, works in the browser, and requires no account. Use it for geometry, construction, or any task that needs triangle measurements. Remember to use valid side lengths that satisfy the triangle inequality.