Triangle Height Calculator
A triangle with an area of 30 and a base of 10 has a height of 6. This triangle height calculator uses the formula area equals one half times base times height to solve for any one of the three values when the other two are known. Enter any two values and the tool returns the third. Finding the height of a triangle is one of the most common geometry tasks, but it trips people up because the height is not always drawn on the diagram. The height is the perpendicular distance from the base to the opposite vertex, not the length of a slanted side. If you already know a triangle's area and either its base or its height, the formula rearranges cleanly to give you the missing number without measuring anything. This tool automates that rearrangement so you do not need to remember whether to multiply or divide by 2.
Quick answer
The formula area = 1/2 x base x height relates the three measurements of any triangle, not just right triangles, because the height is always measured perpendicular to the base.
Enter exactly two positive values and leave the third empty.
What this tells you
- •The formula area = 1/2 x base x height relates the three measurements of any triangle, not just right triangles, because the height is always measured perpendicular to the base.
- •To solve for area, multiply base by height and divide by 2. This is the standard triangle area formula taught in geometry.
- •To solve for height, multiply area by 2 and divide by base. This rearrangement is what makes this tool useful when the height is not drawn on the diagram.
- •To solve for base, multiply area by 2 and divide by height. The same logic works in all three directions.
- •All values must be positive numbers and use the same unit. Mixing inches and centimeters will give a wrong answer.
- •The result uses the same unit system as the inputs with no unit conversion applied. Area is always in square units.
- •This tool fills the same role as solving for a missing side in the triangle area formula by hand, just faster and without the risk of dividing when you should have multiplied.
How to Use
- 1Enter the two values you know, area and base, area and height, or base and height.
- 2Leave the unknown field empty. The calculator solves for that missing value.
- 3The formula used depends on which field is left empty, so double-check that the correct field is blank.
- 4Read the result. The solved value appears in the same unit as the inputs.
How It Works
Formula
area = 1/2 x base x heightThe area of any triangle equals half the product of its base length and its height, where height is the perpendicular distance from the base to the opposite vertex. When area and one side are known, the formula is rearranged: height equals 2 times area divided by base, and base equals 2 times area divided by height. This is the same relationship used in the area formula for all triangles, not just right triangles, as long as the height is measured perpendicular to the base.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Solve for area
Multiply 10 by 6 to get 60, then divide by 2 to get 30 square units.
Solve for height
Multiply 30 by 2 to get 60, then divide by the base of 10 to get a height of 6.
Solve for base
Multiply 30 by 2 to get 60, then divide by the height of 6 to get a base of 10.
Sample Base, Height, and Area Pairs
| Base | Height | Area |
|---|---|---|
| 10 | 6 | 30 |
| 8 | 5 | 20 |
| 12 | 4 | 24 |
| 15 | 8 | 60 |
Common mistakes
- Using a slant side length instead of the perpendicular height. The height must be measured at a right angle to the base.
- Forgetting to divide by 2. The formula is half base times height, not base times height.
- Mixing units. Both base and height must use the same unit before calculating.
Embed this calculator on your site
Drop this single line where you want the calculator to appear. It is responsive, mobile-friendly, resizes automatically, and is free to use with attribution.
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