Triangle Area Calculator

A = b × h ÷ 2

Base

Any one of the three sides, in centimetres. Which one you pick does not matter as long as the height is measured against that same side

Height

The perpendicular distance from the base up to the opposite corner, in centimetres — measured at a right angle to the base, never along a sloping side

Area

How much surface the triangle encloses, in square centimetres. Half of what a parallelogram with the same base and height would cover

Two

The divisor, and the whole reason the formula is not simply base times height. A triangle is half of the parallelogram made by turning a copy of it half a turn

b × h

The area of that parallelogram, computed first and halved afterwards. Doing the multiplication before the division is what keeps the last digit right when the numbers are not whole

Four decimal places

How wide the reading is written. Halving an exact product can leave a fraction — a base of 7 with a height of 5 gives 17.5, and a half-centimetre base gives a quarter

Square centimetres

The unit of the answer whatever the dropdown says. An area is always in squared units, so a base and height given in inches come back as a square-centimetre figure that has to be divided by 6.4516 to be read in square inches

This page answers the area question for any shape that is a triangle, whatever it is made of and however it is drawn. Land is the oldest use: a plot that comes to a point is a triangle, and a plot with four corners is two triangles, which is why surveyors have worked this way for as long as there have been deeds. Roofing, cladding and glazing are the modern ones, and they all bring a bill with them — a gable end, a triangular pane, a wedge of sheet metal, each priced per square metre, so the area has to be right before the order goes in. Fabric and paper cut on the diagonal are the same calculation with a different unit, and so is the sail of a boat or the triangular face of a pyramid. It is also the second half of a great many other jobs. Any polygon can be split into triangles, and once you can do one of them the rest is arithmetic — which is why this formula turns up inside calculators for quadrilaterals, prisms and roofs, and why it is worth being sure of it on its own. And there is the classroom version: right-angled triangles, isosceles ones, the ones drawn on squared paper where you can count the squares and check the answer yourself. That check is worth doing once, because seeing that the count and the formula agree is what makes the halving stop being a rule to remember.

1. A base of 10 and a height of 6

   1. Multiply the base by the height: 10 × 6 = 60
   2. Halve it: 60 ÷ 2 = 30

   The pair the page loads with, and the row that shows the relationship to the parallelogram: enter the same base and height as a parallelogram and you get 60, which is exactly twice this. If you remember one number from this page, remember that one — it is the fastest way to tell whether a triangle answer you have been given is plausible.

2. A base of 7 and a height of 4

   1. Multiply the base by the height: 7 × 4 = 28
   2. Halve it: 28 ÷ 2 = 14

   The ordinary case: an odd base, an even height, and a whole-number answer. Nothing here is a special shape and nothing had to be measured at a convenient angle. This is what most real triangles look like — a rough plot, a gable end, a piece of card cut at an angle — and the formula does not care that the sides are uneven.

3. A base of 5 and a height of 8

   1. Multiply the base by the height: 5 × 8 = 40
   2. Halve it: 40 ÷ 2 = 20

   The row to compare with the trapezoid page. Give a trapezoid a top base of zero, a bottom base of 10 and a height of 4 and you get 20 — the same number, because a trapezoid with one base of zero is a triangle. The two pages print the same figure for the same shape, which is the point of having both.

4. A base of 12.5 and a height of 8

   1. Multiply the base by the height: 12.5 × 8 = 100
   2. Halve it: 100 ÷ 2 = 50

   A measurement with a decimal in it, which is what a tape measure usually gives. The multiplication happens before the halving and the halving is exact, so no rounding error creeps in at all — the answer is 50 exactly, not 50.0000-something.

5. A base of 20 and a height of 0

   1. Multiply the base by the height: 20 × 0 = 0
   2. Halve it: 0 ÷ 2 = 0

   A height of zero means the triangle has been flattened onto its own base and is now a line segment. Zero is a legal input, so this is a real answer rather than a missing one — the page distinguishes it from leaving a box empty, which shows no result at all because there is nothing to work from.

This page takes a base and a perpendicular height and nothing else. It will not work from the three sides of a triangle, which is a different calculation with its own formula and its own page. It gives no perimeter, no angles and no side lengths, and the height is not a sloping side — if the only measurement you have is along one of the triangle's edges, that edge has to be turned into a perpendicular height before it is any use here. The answer is always in square centimetres whatever unit the dropdown is set to, and since this is an area, the conversion is squared: a base and height entered in inches come back as square centimetres, and to read that in square inches you divide by about 6.45 rather than by 2.54. Four decimal places is a display width rather than a claim about precision, and half of an exact product can genuinely be a fraction — a base of 7 with a height of 5 gives 17.5. Zero is accepted for either input and gives an answer of zero, which is right for a degenerate triangle and is not the same as leaving the boxes blank. Nothing here handles a curved side, a triangle drawn on a sphere, or the thickness of a piece of material — this is the flat, two-dimensional figure only.

Which side is the base?

Any of the three, as long as the height is measured against the one you picked. A triangle has three possible base-and-height pairs and all three give the same area, which is a good check to run once: take a triangle, work the area from each corner in turn, and watch the three answers agree. The page does not mind which pair you use.

Why is the answer half of base times height?

Because two copies of a triangle make a parallelogram. Take the triangle, copy it, turn the copy half a turn and join the two along a matching side — the shape you get has the same base and the same height and exactly twice the area. The triangle is half of it. That is the entire argument, and it holds for every triangle, not only for the tidy ones.

Can I use a sloping side as the height?

No, and this is the mistake the page exists to prevent. The height is the perpendicular distance from the base up to the opposite corner, measured at a right angle to the base. A sloping side is longer than that distance whenever the triangle leans, so using it inflates the area. The two numbers are equal only in a right triangle, where one of the sides happens to stand at a right angle to the base already.

Where is the three-sides version?

On its own page. Working out a triangle's area from its three side lengths uses a different formula and a square root rather than a halving, and it is a separate tool. This page deliberately does one thing, which is the same choice the circle and sphere pages in this group make: a page that answers one question is easier to use than a page that asks you which of several questions you meant.

Do the units matter?

The unit dropdown changes what you type in, not what comes out. The reading is always in square centimetres, and because this is an area the conversion is squared — a triangle measured in inches comes back as a square-centimetre figure, and you divide by 6.4516 to read it in square inches. Entering feet and reading the answer as square feet is the error to watch for.

What if one of the numbers is zero?

The answer is zero, and that is correct: a triangle with no height has been flattened onto its base and covers nothing. Zero is treated as a real value rather than as an empty box, so the page prints a result. Leaving a box blank is different — there is nothing to work from and the page shows no result at all.

• Triangle Area — the half-base-times-height formula this page computes, with the parallelogram argument that shows why the halving is there — Wolfram MathWorld (United States)
• Triangle — what a triangle is, the vocabulary of base and altitude, and the several ways its area can be arrived at — Wolfram MathWorld (United States)
• Parallelogram — the shape two copies of a triangle make, whose area is exactly double, and the reason the divisor in the formula is two — Wolfram MathWorld (United States)
• 教育部关于印发义务教育课程方案和课程标准（2022 年版）的通知——The fifth item in the annex list of this notice is the Mathematics Curriculum Standards for Compulsory Education (2022 edition); the area of a triangle is part of the compulsory-education mathematics curriculum, and the wording of the standards and the grade-band breakdown are governed by that annex — 中华人民共和国教育部