Triangle Area Calculator

SCALENE TRIANGLE

Calculate triangle area from side and height.

Triangle area from side and height
SΔ = 12a × h
Side of triangle a
Height of triangle h
Result:

Calculate triangle area from two sides and the included angle.

Triangle area from two sides and included angle
SΔ = 12a × b × sin(α)
Side of triangle a
Side of triangle b
Angle between sides α
Result:

Calculate triangle area from three sides using Heron's formula.

Triangle area from three sides
p = (a + b + c)2
SΔ = √p(p-a)(p-b)(p-c)
Side of triangle a
Side of triangle b
Side of triangle c
Result:

Calculate triangle area from the inscribed circle radius and semiperimeter.

Triangle area from inscribed radius and semiperimeter
p = (a + b + c)2
SΔ = p × r
Inscribed circle radius r
Triangle semiperimeter p
Result:

Calculate triangle area from three sides and circumscribed circle radius.

Triangle area from three sides and circumradius
SΔ = a × b × c4 × r
Side of triangle a
Side of triangle b
Side of triangle c
Circumscribed circle radius r
Result:

Calculate triangle area from a side and two adjacent angles.

Triangle area from side and two adjacent angles
SΔ = a² × sin(β) × sin(γ) 2 × sin (β + γ)
Side of triangle a
Angle between sides β
Angle between sides γ
Result:

Calculate triangle area from a side and all three angles.

Triangle area from side and three angles
SΔ = a² × sin(β) × sin(γ) 2 × sin (α)
Side of triangle a
Angle α
Angle β
Angle γ
Result:

ISOSCELES TRIANGLE

Calculate triangle area from two sides and the included angle (isosceles).

Isosceles triangle area from sides and angle
SΔ = 12a² × sin(β)
Side of triangle a
Angle α
Result:

Calculate triangle area from base length and base angle (isosceles).

Isosceles triangle area from base and base angle
SΔ = 12b² × tg(α)
Triangle base b
Angle at base α
Result:

Calculate triangle area from base length and vertex angle (isosceles).

Isosceles triangle area from base and vertex angle
SΔ = b²4 × tg (β/2)
Triangle base b
Vertex angle β
Result:

Calculate triangle area from side and height drawn to base (isosceles).

Isosceles triangle area from side and height to base
SΔ = h × √a² - h²
Side of triangle a
Height drawn to base h
Result:

Calculate triangle area from base length and height drawn to base (isosceles).

Isosceles triangle area from base and height to base
SΔ = 12b × h
Triangle base b
Height drawn to base h
Result:

EQUILATERAL TRIANGLE

Calculate triangle area from side length (equilateral).

Equilateral triangle area from side
SΔ = a² × √3 4
Side of triangle a
Result:

Calculate triangle area from height (equilateral).

Equilateral triangle area from height
SΔ = h² √3
Height of triangle h
Result:

Calculate triangle area from inscribed circle radius (equilateral).

Equilateral triangle area from inscribed radius
SΔ = 3 × √3r²
Inscribed circle radius r
Result:

Calculate triangle area from circumscribed circle radius (equilateral).

Equilateral triangle area from circumradius
SΔ = 3 × √3r² 4
Circumscribed circle radius r
Result:

RIGHT TRIANGLE

Calculate right triangle area from the two legs.

Right triangle area from legs
SΔ = 12a × b
Legs a
Legs b
Result:

Calculate right triangle area from a leg and the hypotenuse.

Right triangle area from leg and hypotenuse
SΔ = 12a × √c² - a²
Legs a
Hypotenuse c
Result:

Calculate right triangle area from the hypotenuse and acute angle.

Right triangle area from hypotenuse and acute angle
SΔ = 14c² × sin(2α)
Hypotenuse с
Angle between sides α
Result:

Calculate right triangle area from a leg and adjacent acute angle.

Right triangle area from leg and adjacent acute angle
SΔ = 12a² × tg(α)
Legs a
Adjacent acute angle α
Result:

Calculate right triangle area from hypotenuse and inscribed circle radius.

Right triangle area from hypotenuse and inscribed radius
SΔ = r × (r + c)
Hypotenuse c
Inscribed circle radius r
Result:

Calculate right triangle area where the inscribed circle splits the hypotenuse.

Right triangle area from tangent and hypotenuse segments
SΔ = с1 × с2
Hypotenuse segment c1
Hypotenuse segment c2
Result:

A triangle is a closed shape with three sides, three angles, and three vertices. Interior angles always sum to 180°. Triangles are classified by angles — acute (all < 90°), right (one = 90°), obtuse (one > 90°) — and by sides — equilateral (all equal), isosceles (two equal), scalene (all different).

The area of a triangle is the region enclosed by its three sides, measured in square units. Twenty-three formula variants cover virtually any combination of known measurements you might have.

Core Area Formulas

Side and height: S = ½ x a x h. The simplest formula — pick any side as base and multiply by its corresponding height.

Two sides and included angle: S = ½ x a x b x sin(C). Uses the sine of the angle between two known sides.

Heron's formula (three sides): S = √(p(p-a)(p-b)(p-c)), where p = (a+b+c)/2 is the semiperimeter. Works for any triangle when all three sides are known.

Inscribed circle: S = p x r, where p is semiperimeter and r is the inradius.

Circumscribed circle: S = abc / 4R, where R is the circumradius.

Right Triangle Shortcuts

For right triangles, the legs serve as base and height: S = ½ x leg1 x leg2. This eliminates the need to find a separate height.

Applications

Construction: Calculate gable end areas, roof truss triangles, and plot measurements.

Land surveying: Determine irregular land area by triangulation.

Engineering: Compute cross-sectional areas for structural members and truss designs.

Education: Practice with multiple area formulas and understand their mathematical equivalence.

SΔ = 12a × h
SΔ = 12a × b × sin(α)
p = (a + b + c)2
SΔ = √p(p-a)(p-b)(p-c)