Triangle Calculator
Calculate the area of any triangle from its base and height or from its three sides, and find a missing side of a right triangle. Pick a mode, type the numbers and the answer updates instantly.
How to use the triangle calculator
- Choose a mode: area from base and height, area from three sides, or right triangle.
- Enter the values the mode asks for, such as the base and height or the side lengths.
- Read the area or the solved side from the result card.
Examples
Area from base and height
base = 8, height = 5
Area = 20
Right triangle (3-4-5)
leg a = 3, leg b = 4
Hypotenuse c = 5
Frequently asked questions
How do you find the area of a triangle?
The simplest formula is area = ½ × base × height, where the height is measured straight down from the opposite vertex to the base. If you know the three side lengths instead, use Heron's formula.
What is Heron's formula?
Heron's formula finds the area from the three side lengths a, b and c with no height needed. Compute the semi-perimeter s = (a + b + c) / 2, then area = sqrt(s(s − a)(s − b)(s − c)).
What is the Pythagorean theorem?
For a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c², where c is the hypotenuse. Rearranged, a leg is sqrt(c² − b²).
What is the triangle inequality?
A triangle can only exist if the sum of any two sides is greater than the third side. If three lengths fail this test, no triangle is possible, so the area from three sides is rejected.
Why must the hypotenuse be the longest side?
In a right triangle the hypotenuse sits opposite the right angle and is always the longest side. If you ask to solve a leg but give a hypotenuse shorter than the known leg, no real triangle exists.
Is my data sent anywhere?
No. Every calculation runs in your browser, so the numbers you type are never uploaded or stored.
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