Triangle Area Calculator
Press Calculate to see the area, the working and other units.
Find the area of any triangle from whatever you can measure: base and height, all three sides, two sides and the angle between them, or two angles and the side between them.
Every method here gives the same kind of answer, so choose by what you can actually measure. On paper, base and height is usually simplest. On a plot of land or a sloping roof, the height is often hard to reach, and three tape measurements along the sides are far more practical.
Formula
A = ½ × b × h
- A
- the area
- b
- the length of any side, used as the base
- h
- the height, measured at right angles to that base
Area from base and height
A triangle fills exactly half of the parallelogram built from two copies of it, which explains the one half in the formula. Any side can serve as the base, but the height must be perpendicular to the side you pick. A triangle with a base of 12 cm and a height of 5 cm covers ½ × 12 × 5 = 30 cm².
The commonest mistake is using a slanted side as the height. The two only match in a right triangle, where the two shorter sides meet at 90°. A right triangle with sides of 3, 4 and 5 has an area of ½ × 3 × 4 = 6.
Area from three sides (Heron's formula)
Heron's formula needs no height or angle. Add the three sides and halve the total to get s, the semi-perimeter, then take the square root of s(s − a)(s − b)(s − c). For sides of 5, 6 and 7, s is 9 and the area is √(9 × 4 × 3 × 2) = √216 ≈ 14.70.
Three lengths only make a triangle when each is shorter than the other two added together. Lengths of 2, 3 and 10 cannot close up, so the calculator reports an error rather than a meaningless number.
- A = √( s(s − a)(s − b)(s − c) )
- s = (a + b + c) ÷ 2
Area from two sides and an angle
When you know two sides and the angle between them, multiply the sides, multiply by the sine of the angle, and halve the result. Sides of 8 and 11 meeting at 40° give ½ × 8 × 11 × sin 40° ≈ 28.28. The angle has to be the one enclosed by those two sides; an angle elsewhere describes a different triangle.
- A = ½ × a × b × sin C
Area from two angles and a side
Two angles fix the triangle's shape, because the third is whatever remains of 180°. One known side then fixes its size. Using the side between the two angles, a side of 10 with angles of 45° and 60° gives 10² × sin 45° × sin 60° ÷ (2 × sin 105°) ≈ 31.70.
- A = c² × sin A × sin B ÷ (2 × sin(A + B))
Frequently asked questions
How do I find the area of a triangle with 3 sides?
Use Heron's formula. Halve the sum of the sides to get s, then take the square root of s(s − a)(s − b)(s − c). Choose the 3 sides option above and the calculator does this for you.
How do I find the area of an irregular or scalene triangle?
The same formulas work for every triangle, whatever its side lengths. Measure all three sides and use Heron's formula, since no right angle or equal sides are required.
Can I use different units for each side?
Yes. Each input has its own unit menu. The calculator converts them all before solving and reports the area in the square of the first input's unit.
Why does the calculator say my sides cannot form a triangle?
The longest side must be shorter than the other two combined. If it is equal or longer, the sides cannot meet to enclose any area, so it is worth re-measuring.
What is the area of an equilateral triangle?
With all sides equal to s, the area is √3 ÷ 4 × s². A triangle with sides of 10 has an area of about 43.30, and the 3 sides option gives the same value.
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