Base Of A Triangle Calculator

Background.

A triangle's area pins down far less than its shape. Know the area and the perpendicular height and exactly one base length fits, yet an endless family of triangles shares that base and height: slide the top corner sideways along a line parallel to the base and the area never changes. That is why the base can be found from just two numbers, and why those two numbers say nothing about the other two sides.

The relationship comes straight from the area formula learned in school, area = ½ × base × height. Undo it and base = 2 × area ÷ height. The factor of two is there because a triangle is exactly half of a parallelogram with the same base and height.

The one thing that has to be right is what "height" means. It is the perpendicular distance from the corner opposite the base to the line the base lies on, not the length of a sloping side. In a right triangle the two legs serve as each other's heights, so the shortcut works directly. In an obtuse triangle the height belonging to either of the two sides that meet at the obtuse angle falls outside the figure, landing on the base extended, and it is still the right number to use. Putting a slanted side into the height field always produces a base that is too short, because any slanted line from a corner to the base line is longer than the perpendicular.

Units follow the height. Enter the area in square metres and the height in metres and the base comes out in metres; pair square metres with a height in centimetres and the result is wrong by orders of magnitude.

What is base of a triangle calculator?

The base of a triangle is whichever side you choose to measure the height from; nothing makes the bottom edge special. Every triangle has three possible bases, each paired with its own height, the perpendicular distance from the opposite vertex to the line containing that side. Each pair satisfies base × height = 2 × area, so a long side always pairs with a short height and a short side with a tall one. Given the area and one height, the matching base is the single length that makes that product come out right.

How to use this calculator.

1. 01Enter the triangle's area in Triangle area, in square units: square centimetres, square feet, square metres or whatever your source uses.
2. 02Enter the perpendicular distance from the vertex opposite the side you want to the line of that side, in the matching linear unit. Measure it at a right angle, never along a sloping edge.
3. 03If that perpendicular lands outside the triangle, as it does for the two sides meeting at an obtuse angle, measure to the side's line extended and enter that distance.
4. 04Read the base in the same unit as the height, and check it by multiplying base × height ÷ 2 to get the area back.

The formula.

Base = 2 × area ÷ height, which is A = ½ b h rearranged for b. Two identical copies of any triangle fit together into a parallelogram whose area is base × height, so the triangle has half of it; multiplying the area by 2 recovers the parallelogram, and dividing by its height leaves its base. The base is inversely proportional to the height: halve the height at a fixed area and the base doubles, which is why very flat triangles have very long bases. Area and height must be in matching units, square centimetres with centimetres or square feet with feet, and the result comes out in that linear unit. The only assumption is that the height entered is genuinely perpendicular to the side being found; the other two sides and the angles play no part.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.