Triangle Square Footage Calculator

A triangle's area is half of its base times its height. That's the whole formula. The part people get wrong is the height, which has to be the straight-up perpendicular distance to the point, not the length of a slanted side. Enter your numbers below for the answer, and read on for how to handle the case where you only know the three side lengths.

The basic formula

For any triangle:

Area = (base × height) ÷ 2

Pick any one side as the base. The height is the perpendicular distance from that base straight to the opposite corner. If your measurements are in feet, the answer comes out in square feet with no conversion needed. If you measured in inches, multiply base and height in inches, then divide by 144 to get square feet.

The reason you divide by two is simple. Any triangle is exactly half of the rectangle you'd draw around its base and height. Full rectangle is base times height; the triangle is half of it.

Base and height, and why the slanted side is a trap

The height is the tricky measurement. It is measured at a right angle to the base, straight to the far point. It is not the length of one of the other two sides unless that side happens to be vertical.

Picture a right triangle sitting on one leg. The two legs meet at 90 degrees, so one leg is the base and the other leg is the height. Easy. But on a leaning or slanted triangle, the height is a line you often have to drop from the top corner down to the base at a right angle, and it can even fall outside the triangle for very stretched shapes. When in doubt, measure the true vertical drop from the peak to the base line, not the sloping edge.

Right triangle vs non-right triangle

A right triangle is the friendly case. One corner is a square 90 degree corner, and the two sides that form it, the legs, are already a base and height at right angles to each other. Measure both legs, multiply, halve, done. A corner countertop cut on the diagonal or a square patio sliced corner to corner both give you right triangles.

A non-right triangle has no square corner, so neither of the two non-base sides is the true height. You have three options: measure the perpendicular height directly with a level or framing square, split the shape into two right triangles and add them, or skip height entirely and use Heron's formula with the three side lengths. For an odd triangle the three-sides route is usually the least fiddly.

Base and height reference table

If you already have a clean base and height, this table saves the arithmetic. Every value is base times height divided by two.

Base	Height	Area (sq ft)
10 ft	8 ft	40
12 ft	6 ft	36
16 ft	8 ft	64
20 ft	10 ft	100
24 ft	6 ft	72
24 ft	12 ft	144
30 ft	20 ft	300

A triangle is always exactly half the rectangle of the same base and height, so the 24 by 12 triangle covers 144 square feet, the same as a 12 by 12 square room.

Worked example 1: base and height

Say you're paneling the gable end of a wall, the triangular part above the square section, and it spans 24 feet across the bottom and rises 6 feet to the peak.

Base = 24 ft, height = 6 ft.
Area = (24 × 6) ÷ 2 = 144 ÷ 2 = 72 square feet.

That's the siding or drywall area for the triangle alone. Add it to the rectangular wall below it to get the whole gable. For a two-piece wall like this, the room calculator and the how to calculate square footage guide show how to add a rectangle and a triangle together.

Finding the height of a gable from the roof pitch

Gable walls are the most common triangle people measure, and the peak is usually 15 or 20 feet in the air where you can't reach a tape to it. The workaround is to get the height from the roof pitch instead.

Roof pitch is written as rise over run, like 6/12, which means the roof climbs 6 inches for every 12 inches it runs horizontally. The peak sits over the center of the wall, so the run from the eave to the center is half the wall's width. Multiply that run by the pitch rise and you have the height.

Example. The gable wall is 24 feet wide and the roof is a 6/12 pitch. Half the width is 12 feet of run. At 6/12, the roof rises 6 inches, or 0.5 feet, per foot of run. Height = 12 × 0.5 = 6 feet. Base 24, height 6, area = (24 × 6) ÷ 2 = 72 square feet, the same gable as above but reached without a ladder to the peak. A steeper 12/12 pitch on the same wall would rise a full foot per foot of run, giving a 12 foot height and 144 square feet.

Heron's formula: when you only know the three sides

Sometimes you can't measure a clean height. A triangular garden bed, an odd corner of a room, or a survey lot might give you three side lengths and nothing else. Heron's formula handles exactly that case, using only the sides.

First find the semi-perimeter, which is half the total distance around the triangle:

s = (a + b + c) ÷ 2

Then:

Area = √( s × (s − a) × (s − b) × (s − c) )

Here a, b, and c are the three side lengths. The formula works for any triangle, and it's the same math the Math Open Reference and Omni Calculator triangle tools use behind the scenes.

Worked example 2: Heron's formula

You've laid out a triangular flower bed with sides of 13 feet, 14 feet, and 15 feet, and there's no obvious base and height to measure.

Semi-perimeter: s = (13 + 14 + 15) ÷ 2 = 42 ÷ 2 = 21.
Plug in: Area = √( 21 × (21 − 13) × (21 − 14) × (21 − 15) ).
That's √( 21 × 8 × 7 × 6 ) = √7,056.
√7,056 = 84 square feet.

So the bed covers 84 square feet. The whole point of Heron's formula is that you don't have to measure the height at all. Three sides is enough.

Worked example 3: a second Heron's calculation

Another one with different numbers. A triangular patch of lawn has sides of 9, 10, and 17 feet.

Semi-perimeter: s = (9 + 10 + 17) ÷ 2 = 36 ÷ 2 = 18.
Area = √( 18 × (18 − 9) × (18 − 10) × (18 − 17) ).
That's √( 18 × 9 × 8 × 1 ) = √1,296.
√1,296 = 36 square feet.

This triangle is long and thin, since one side (17 feet) is almost as long as the other two combined. Heron's formula handles that fine, where eyeballing a height would have been hopeless.

Worked example 4: a triangular lot

A corner lot comes back from the survey as a triangle with boundary lengths of 130, 140, and 150 feet. No height, just the three sides, which is exactly what a plat gives you.

Semi-perimeter: s = (130 + 140 + 150) ÷ 2 = 420 ÷ 2 = 210.
Area = √( 210 × (210 − 130) × (210 − 140) × (210 − 150) ).
That's √( 210 × 80 × 70 × 60 ) = √70,560,000.
√70,560,000 = 8,400 square feet.

At 8,400 square feet, that lot is 8,400 ÷ 43,560 = about 0.19 acres, a step our square footage to acres converter handles for you (1 acre = 43,560 sq ft).

Where triangle square footage comes up

Gable walls and rooflines. The triangular end of a wall, a dormer, or a roof plane. Base times height over two, with the height often coming from the roof pitch rather than a tape.

Triangular and pie-shaped lots. Corner lots and odd parcels are rarely neat rectangles. If a survey gives you the three boundary lengths, Heron's formula gets the area, which you can convert toward acres.

Odd room corners and bay areas. When a room isn't a clean box, the trick most people land on is to break it into rectangles plus a triangle or two and add the pieces, the standard advice repeated in home improvement forums for irregular rooms.

Angled countertops, decks, and patios. A corner counter, a diagonal deck cut, or a triangular patio section is just base times height over two.

Common mistakes

Using a slanted side as the height. The most frequent error. Height is the perpendicular distance to the base, not the length of the sloping edge. Using the slope inflates your answer.

Forgetting to divide by two. Base times height alone gives you the rectangle, which is double the triangle. If your number seems too big, check whether you halved it.

Mixing units. Keep base and height in the same unit. Base in feet and height in inches gives nonsense unless you convert one first.

Using the full wall width as the run for a gable. The run to the peak is half the wall width, because the peak sits over the center. Use the full width and you'll double the height.

Reaching for Heron's formula when base and height are easier. If you can measure a clean height, the simple formula is faster and less error prone.

Frequently asked questions

How do you calculate the square footage of a triangle?

Multiply the base by the height and divide by two. The height must be the perpendicular distance from the base to the opposite point, not a slanted side. A triangle with a 24 foot base and a 6 foot height is (24 × 6) ÷ 2 = 72 square feet.

How do I find the square footage of a triangle when I only know the three sides?

Use Heron's formula. Find the semi-perimeter s = (a + b + c) ÷ 2, then take the square root of s × (s − a) × (s − b) × (s − c). For sides of 13, 14, and 15 feet, s is 21 and the area works out to 84 square feet.

What counts as the base and the height of a triangle?

Any side can be the base. The height is the straight perpendicular distance from that base to the opposite corner, measured at a right angle. On a right triangle the two legs serve as base and height; on a slanted triangle you may have to drop a vertical line from the peak.

What is the difference between a right triangle and a non-right triangle for area?

A right triangle has a 90 degree corner, so its two legs are already the base and height and you can multiply them directly. A non-right triangle has no square corner, so you either measure the perpendicular height, split it into two right triangles, or use Heron's formula with the three sides. The underlying area rule, base times height over two, is the same for both.

How do I find the height of a gable wall I can't reach?

Get it from the roof pitch. Take half the wall width as the run, then multiply by the pitch rise per foot. A 24 foot wide gable with a 6/12 pitch has a 12 foot run and rises half a foot per foot, so the height is 6 feet.

Why do I divide by two when finding a triangle's area?

Because a triangle is exactly half of the rectangle drawn around its base and height. The rectangle's area is base times height, so the triangle is that divided by two.

Does the triangle formula work in any unit?

Yes, as long as the base and height are in the same unit. Feet give square feet directly. If you measure in inches, multiply and then divide by 144 to convert square inches to square feet.

For any other shape or a whole project at once, start from the main square footage calculator.

Triangle Square Footage Calculator