Triangle Area Calculator
Calculate the area of any triangle using its base and height, three side lengths, two sides and their included angle, or the coordinates of its three vertices. Get instant results, formulas, step-by-step working, perimeter and area unit conversions.
Enter the x and y coordinates of each vertex. Coordinates must use the same length unit.
Triangle area calculator with diagram
A triangle is a two-dimensional polygon with three sides and three interior angles. Its area is the amount of space enclosed by those sides. The most common method uses the base and perpendicular height.
A = ½bh
Use when the base and its perpendicular height are known.
A = √[s(s−a)(s−b)(s−c)]
Heron's formula, where s is the semiperimeter.
A = ½ab sin(C)
The angle must be between the two measured sides.
A = ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)|
Calculate area from three points on a coordinate plane.
A = (√3/4)a²
All three sides have equal length.
A = ½ × leg₁ × leg₂
The two perpendicular legs act as base and height.
How to calculate the area of a triangle
1. Using the base and height
Multiply the base by its perpendicular height and divide the result by two. For example, a triangle with a base of 10 metres and a height of 6 metres has an area of 30 square metres.
2. Using three sides (Heron's formula)
When you know all three side lengths but not the height, first calculate the semiperimeter. The semiperimeter is half the sum of the three sides.
A = √[s(s − a)(s − b)(s − c)]
For side lengths of 5, 6 and 7 units, the semiperimeter is 9. The area is √(9 × 4 × 3 × 2), or approximately 14.697 square units.
3. Using two sides and their included angle
If two sides and the angle between them are known, use the sine of that angle. Ensure that the angle is measured in degrees when entering it into this calculator.
4. Using three vertex coordinates
Coordinates can be used even when the triangle is rotated or one of its angles is obtuse. Enter all three points in the same coordinate system and use the determinant formula to calculate the absolute area.
Triangle area examples
| Triangle type | Measurements | Area formula | Area |
|---|---|---|---|
| Base and height | b = 10, h = 6 | ½ × 10 × 6 | 30 square units |
| Right triangle | Legs = 3 and 4 | ½ × 3 × 4 | 6 square units |
| Equilateral | Side = 4 | √3 × 4² / 4 | 6.928 square units |
| Three sides | a = 5, b = 6, c = 7 | Heron's formula | 14.697 square units |
| Two sides and angle | a = 8, b = 6, C = 30° | ½ × 8 × 6 × sin(30°) | 12 square units |
These examples use the same arbitrary length unit for every side and height. The resulting areas are expressed in square units.
Triangle area unit conversions
Area conversion factors are squared because area measures two dimensions. The calculator automatically converts your triangle's area into the selected output unit.
| Area unit | Equivalent in square metres | Typical application |
|---|---|---|
| 1 mm² | 0.000001 m² | Small components |
| 1 cm² | 0.0001 m² | Drawings and small surfaces |
| 1 m² | 1 m² | Rooms and surfaces |
| 1 km² | 1,000,000 m² | Large geographical areas |
| 1 in² | 0.00064516 m² | Imperial measurements |
| 1 ft² | 0.09290304 m² | Floor plans |
| 1 yd² | 0.83612736 m² | Construction and landscaping |
| 1 acre | 4,046.8564224 m² | Land measurements |
| 1 hectare | 10,000 m² | Agriculture and land areas |
Understanding triangle area and perimeter
Area and perimeter measure different properties. Area describes the two-dimensional space enclosed by the triangle. Perimeter is the total length of its three sides.
A = ½bh
Expressed in square units, such as cm² or m².
P = a + b + c
Expressed in linear units, such as cm or m.
s = (a + b + c) / 2
Used in Heron's formula to find area from three sides.
Frequently asked questions
What is the formula for the area of a triangle?
The standard formula is A = ½ × base × perpendicular height. Multiply the base by its perpendicular height and divide by two.
How do I calculate triangle area without the height?
If all three side lengths are known, use Heron's formula: A = √[s(s − a)(s − b)(s − c)], where s is half the sum of the three sides. If two sides and their included angle are known, use A = ½ab sin(C).
Can I calculate the area using only three side lengths?
Yes. Select the three-side method and enter sides a, b and c. The calculator checks whether the lengths can form a valid triangle before applying Heron's formula.
What is the area of an equilateral triangle?
For an equilateral triangle with side length a, the area is A = (√3/4)a². All three sides and all three interior angles are equal.
Does the height have to be inside the triangle?
No. For an obtuse triangle, the perpendicular height to a selected base may fall outside the triangle. The height is still the perpendicular distance from the opposite vertex to the line containing that base.
Can I use different units for the sides?
This calculator assumes all entered lengths use the selected length unit. Convert measurements into a common unit before entering them. Coordinates must also use the same unit.
Why is my triangle area zero or invalid?
A triangle with zero area is degenerate: its vertices lie on a straight line or one of its dimensions is zero. For three side lengths, the sum of any two sides must be greater than the remaining side.
Are my measurements uploaded to a server?
No. The calculations run in your browser using JavaScript. This page does not submit your dimensions to the PHP server or store them in a database.
Can I print or share a calculation?
Yes. Use Print result to print the current page, Copy result to copy the formula and answer, or Copy calculation link to create a URL containing your selected method and measurements.
Explore more geometry calculators
Continue with another area calculator or explore additional geometry tools on Superficie.org.