What this calculator does
The usual triangle area formula, area equals half the base times the height, runs forward: you know the base and height and want the area. This calculator runs it backwards. Given the area and the height, it rearranges the formula to solve for the base, which is the question people actually have when a project already states an area and a height and leaves the base unknown.
The rearrangement is simple algebra: multiply the area by two, then divide by the height. That undoes the "half" and the "times height" in the original formula, leaving the base on its own. The calculator also checks the answer by recomputing the area from the base and height it just found, so you can confirm the two numbers are consistent.
The formula
Area = ½ × base × height, so base = (2 × area) ÷ height. Double the area to cancel the one-half, then divide by the height to isolate the base.
| Term | Meaning |
|---|---|
| Base | The side of the triangle the height is measured perpendicular to. |
| Height | The perpendicular distance from the base to the opposite vertex, not the length of a slanted side. |
| Area | The total space enclosed by the triangle. |
The inputs explained
| Field | What to enter |
|---|---|
| Area | The known area of the triangle, in square units. |
| Height | The known perpendicular height, in the same length units as the base you want back. |
When to use it
Working from a stated area
A worksheet, a land survey or a design spec sometimes states a triangle's area and height and leaves the base to be worked out, which is exactly what this reverses.
Checking a cut or a cross-section
If a triangular panel needs a known area and you have already fixed the height, this gives the base length to cut to before you touch the material.
Verifying by hand
Because the calculator also recomputes the area from the base and height it found, it doubles as a check that a hand calculation was done correctly.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What base does a given area and height produce?
A few area and height pairs and the base each one implies.
How does base change as height changes, for a fixed area?
The same area of 36, spread across a range of heights.
Questions
How do you find the base of a triangle?
Rearrange the standard area formula: base = (2 × area) ÷ height. You need the area and the perpendicular height; the base cannot be found from the area alone.
What is the base of a triangle?
It is whichever side the height is measured perpendicular to. Any of the three sides can be called the base, as long as the height used is the perpendicular distance from that side to the opposite corner.
Can this find the base from the area and a slanted side instead of the height?
No. The formula needs the true perpendicular height. Using a slanted side length in its place will give the wrong base, since it is longer than the perpendicular distance.
What if the height is zero?
A height of zero collapses the triangle into a flat line with no area, so no valid base can be found. Enter a positive height greater than zero.
To go the other direction, computing area from a known base and height (or from three sides, or two sides and an angle), see the triangle area calculator.