Triangle Area Calculator
Use this free area of triangle calculator to find the area from whatever measurements you already have: base and height, all three sides with Heron's formula, or two sides plus the angle between them. Results update instantly as you type, and every step of the math is shown so you can check the work.
Enter your numbers
Pick what you know about the triangle — the calculator switches formulas automatically. Results update as you type.
Your results
How to use this calculator
Start by choosing which measurements you have. Base & height is the everyday case: measure any side as the base, then measure the height straight across from it — the height is the shortest distance to the opposite corner, at a right angle to the base. The other two modes handle cases where you don't have a height: Three sides uses Heron's formula when you know all the edges, and Two sides + angle works when you know two edges and the angle between them.
Everything recalculates the moment you type, so you can play with the numbers — change a side length and watch the area move. The result panel always shows which formula was used and the exact substitution, so nothing is a black box.
If your inputs can't describe a real triangle — for example three sides that violate the triangle inequality, or an angle that isn't between 0° and 180° — you'll get a plain-language error explaining the problem instead of a wrong answer.
How it works
The classic formula is A = (b × h) ÷ 2: a triangle is half of the rectangle (or parallelogram) built on the same base and height, so it takes exactly half the rectangle's area. It doesn't matter which side you call the base — as long as the height is perpendicular to that base, the answer is the same.
When you only know the three sides, Heron's formula works without any height at all. First compute the semiperimeter — half the perimeter — s = (a + b + c) ÷ 2, then A = √(s(s − a)(s − b)(s − c)). It only makes sense for valid triangles: the two shorter sides must add up to more than the longest one (the triangle inequality), otherwise the expression under the square root goes negative and no triangle exists. For a 3-4-5 right triangle, s = 6 and A = √(6 × 3 × 2 × 1) = 6 — the same answer you'd get from (3 × 4) ÷ 2.
The third mode uses A = ½ × a × b × sin(C), where C is the angle between sides a and b. The trick behind it: the height relative to side a is just b × sin(C), which turns the formula into the base-and-height form. Your angle must be in degrees here (the calculator converts to radians internally), and it has to be strictly between 0° and 180° — at 0° or 180° the triangle flattens to a line with zero area.
Assumptions: all lengths are positive and in the same unit; the result is in square units of that unit (cm², in², ft², …). Angles are in degrees. These are exact mathematical results, not estimates.
Frequently asked questions
How do you find the area of a triangle?
Multiply the base by the height and divide by 2: A = (b × h) / 2. The height must be measured perpendicular (at 90°) to the base you choose. For example, a triangle with base 10 and height 6 has an area of 30.
What is Heron's formula?
Heron's formula finds the area from the three side lengths. First compute the semiperimeter s = (a + b + c) / 2, then A = √(s(s − a)(s − b)(s − c)). For a 3-4-5 triangle, s = 6 and the area is √(6 × 3 × 2 × 1) = 6.
How can three sides fail to form a triangle?
If the two shorter sides don't add up to more than the longest side, no triangle exists — for example sides 2, 3, and 10. This is the triangle inequality, and this calculator checks it before applying Heron's formula, so you'll get a clear error instead of a nonsense number.
What is the area with two sides and the included angle?
Use A = ½ × a × b × sin(C), where C is the angle between sides a and b. For sides 5 and 7 with a 60° angle between them, the area is 0.5 × 5 × 7 × sin(60°) ≈ 15.155.
Do all three methods give the same area?
Yes — for the same triangle, base × height ÷ 2, Heron's formula, and ½ab·sin(C) all compute the same value. They just start from different known measurements. If two methods disagree, the inputs can't belong to the same triangle.