Base of a Triangle Calculator
Find the base of a triangle when you know its area and height. Rearranging the standard area formula (Area = ½ × base × height) gives base = 2 × area ÷ height. Enter the area and the perpendicular height and the calculator returns the matching base length.
Formula
base = 2 × area ÷ height
- Comes from rearranging the triangle area formula: Area = ½ × base × height.
- Solving for base gives base = 2 × area ÷ height.
- The height must be the perpendicular distance from the base to the opposite vertex — not a slanted side.
- Area and height must use matching units (e.g. cm² with cm) so the base comes out in the same length unit.
Area = 24, height = 6
Inputs
- Area: 24 sq units
- Height (perpendicular): 6 units
base = 2 × 24 ÷ 6 = 48 ÷ 6 = 8 units. So a triangle with area 24 and height 6 has a base of 8.
Frequently asked questions
How do I find the base of a triangle?
If you know the area and the perpendicular height, use base = 2 × area ÷ height.
Why multiply the area by 2?
Because the area formula has a factor of one half: Area = ½ × base × height. Rearranging to solve for base cancels the half by multiplying both sides by 2.
Does this work for any triangle?
Yes — as long as the height is measured perpendicular to the base you're solving for. It works for scalene, isosceles and right triangles alike.
What units does the base come out in?
The same length unit as your height, provided the area is in the corresponding square unit (for example cm² and cm give a base in cm).