Triangle Area Calculator

1. Choose what you know: base and height, three sides, or two sides and an angle.
2. Enter the measurements the method needs.
3. Read the area of the triangle.
4. See the method used and the perimeter where it applies.

Here is what each result means:

The area of a triangle is the amount of flat space it covers. The best-known formula is half the base times the height, where the height is measured straight up from the base to the opposite corner. So a triangle with base 6 and height 4 has an area of 12.

You do not always know the height, though. If you have the three sides, Heron formula finds the area directly. If you have two sides and the angle between them, another formula uses the sine of that angle. All three give the same area; you just pick the one that matches the measurements you have.

It applies whichever of the three standard formulas fits your inputs.

1. For base and height, halve their product.
2. For three sides, use Heron formula with the semi-perimeter.
3. For two sides and an angle, multiply half their product by the sine of the angle.

For a larger or irregular plot rather than a single triangle, the land area calculator handles general shapes.

Find the area of a triangle with sides 3, 4 and 5.

Calculation: the semi-perimeter is s = (3 + 4 + 5) / 2 = 6. Heron formula gives A = sqrt(6 x 3 x 2 x 1) = sqrt(36) = 6. This is a right triangle, so half of 3 times 4 also gives 6, a useful check.

Match the method to the measurements you have.

All three give the same area for the same triangle. Base and height is simplest when a clean height is available.

The two most common methods suit different situations.

Heron formula is handy for a triangle drawn from three lengths, where finding a height would take extra work.

The Base and Height

Area scales with both. Doubling either doubles the area; doubling both quadruples it.

The Angle Between Two Sides

The area is largest when the two sides are at a right angle and shrinks toward zero as the angle flattens.

The Shape of the Sides

For fixed side lengths the area is fixed, but sides that barely form a triangle enclose very little area.

Geometry Homework

Find an area from whatever measurements a problem gives.

Construction and DIY

Work out material for a triangular section of roof, garden or floor.

Surveying

Break an irregular plot into triangles and add their areas.

1. Using a Slanted Side as the Height

The height must be perpendicular to the base, not a sloping side.

2. Forgetting to Halve

Base times height gives a rectangle. The triangle is half of that.

3. Sides That Cannot Form a Triangle

Each side must be less than the sum of the other two, or no triangle exists.

4. Degrees and Radians

Enter the angle in degrees. Mixing units gives a wrong sine and area.

5. Wrong Method for the Inputs

Pick the method that matches what you actually measured.

The formulas are exact; only the displayed decimals are rounded.

The simplest way is half the base times the height. If you know the three sides, use Heron formula; if you know two sides and the angle between them, use half their product times the sine of the angle.

It finds a triangle area from its three sides. Compute the semi-perimeter s, half the perimeter, then take the square root of s times (s minus a) times (s minus b) times (s minus c).

Multiply half the product of the two sides by the sine of the angle between them. So area equals one half a times b times the sine of the included angle C.

It is the perpendicular distance from a base to the opposite corner, measured at a right angle to the base. It is not the length of a slanting side.

No. Each side must be shorter than the sum of the other two, the triangle inequality. If one side is too long, the three lengths cannot close into a triangle.

Enter the angle in degrees for the two-sides-and-angle method. The calculator converts it internally to work with the sine function.

Yes. For a given triangle, all three formulas give the same area. You simply choose the one that matches the measurements you have.

This tool finds the area of a single triangle. A land area calculator handles larger or irregular plots, often by splitting them into simpler shapes.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Triangle (Wikipedia).
• Area of a triangle (Maths Is Fun).
• Heron's formula (Wikipedia).