Quick answer
The height of a triangle is h = 2A ÷ b. With an area of 20 and a base of 10, the height is 4.
Enter the area and the base. The calculator returns the height.
Related tools: Triangle Calculator: Area, perimeter, angles and type of a triangle from its three sides. 45-45-90 Triangle Calculator: Sides of a 45°-45°-90° triangle from one leg. 30-60-90 Triangle Calculator: Sides of a 30°-60°-90° triangle from the short leg.
How to use the Triangle Height Calculator
- Enter area (above 0).
- Enter base (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Area | A number | > 0 |
| Base | A number | > 0 |
Formula and method
Formula
h = 2A ÷ b
IEEE-754 double precision; shown to at most 6 decimal places.
Rearranged area formula.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Area = 20; Base = 10.
| Result | Value |
|---|---|
| Height | 4 |
Example 2
Inputs: Area = 6; Base = 4.
| Result | Value |
|---|---|
| Height | 3 |
The first line is the headline result (height). IEEE-754 double precision; shown to at most 6 decimal places.
Rearranging the area formula
From A = ½bh, h = 2A ÷ b = 40 ÷ 10 = 4. The height is measured perpendicular to the chosen base, and each side of a triangle has its own height.
Checks
For a right triangle with legs 3 and 4, the height to the hypotenuse 5 is 2 × 6 ÷ 5 = 2.4. Values must be positive.
Each side has its own height
A triangle has three heights, one for each side used as the base. With area 20 and base 10 the height is 2 × 20 ÷ 10 = 4; taking base 8 instead gives 2 × 20 ÷ 8 = 5.
In an obtuse triangle the height to the longest side falls inside, but the heights to the other sides meet the extended base outside the triangle. For a 3-4-5 right triangle, area 6, the height to the hypotenuse is 12 ÷ 5 = 2.4.
How the result changes with area
Holding every other input at the first worked example, this table changes only area. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Area | Height |
|---|---|
| 10 | 2 |
| 20 | 4 |
| 40 | 8 |
| 80 | 16 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Base: entering "0" shows "Base must be greater than 0." beside that field and no result.
Choosing between the Triangle Height Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Triangle Calculator](/math/triangle-calculator/) | side a, side b and side c | Area |
| [45-45-90 Triangle Calculator](/math/45-45-90-triangle-calculator/) | leg length | Leg |
| [30-60-90 Triangle Calculator](/math/30-60-90-triangle-calculator/) | short leg length | Short leg |
| [Right Triangle Calculator](/math/right-triangle-calculator/) | leg a and leg b | Hypotenuse c |
| [Triangle Area Calculator](/math/triangle-area-calculator/) | base and height | Area |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Positive values
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for base to confirm this.
Frequently asked questions
What is the height if area is 30 and base 12?
Height = 2 × 30 ÷ 12 = 5.
Is there more than one height?
A triangle has three heights.
Can the height lie outside?
In obtuse triangles, yes.
How do I find a height if I only know the three sides?
Find the area first with Heron's formula, then use h = 2A ÷ b. For a 3-4-5 triangle the area is 6, so the height to the side of length 5 is 2.4.
Does the height depend on which side is the base?
Yes. The area is fixed, so a longer base has a shorter height and a shorter base has a taller one.
What does the Triangle Height Calculator calculate?
Height of a triangle from its area and base. It returns Height.
What formula does the Triangle Height Calculator use?
h = 2A ÷ b. Rearranged area formula.
What do I need to enter in the triangle Height Calculator?
You enter Area and Base.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Positive values.
What is an example of a triangle Height result?
With area 20 and base 10, the height is 4.
Related calculators
- Triangle Calculator — Area, perimeter, angles and type of a triangle from its three sides.
- 45-45-90 Triangle Calculator — Sides of a 45°-45°-90° triangle from one leg.
- 30-60-90 Triangle Calculator — Sides of a 30°-60°-90° triangle from the short leg.
- Right Triangle Calculator — Solve a right triangle from its two legs: hypotenuse, angles, area and perimeter.
- Triangle Area Calculator — Area of a triangle from base and height.
- SAS Triangle Calculator — Solve a triangle from two sides and the included angle.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.