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Triangle Area Calculator

Find a triangle's area from its base and height, three sides, two sides and an angle, or two angles and a side.

Change the values and press Calculate to work out your own figures.

Base and height

Enter the base and height.

The third side.
The perpendicular height.
Result
Area of the triangle
30

The area is 30.

Show the working
  1. A = ½ × base × height

Three sides (SSS)

Enter the three sides.

Opposite angle A.
Opposite angle B.
Opposite angle C.
Result
Area of the triangle
14.69693846
Type
acute scalene
Side a
5
Side b
6
Side c
7
Angle A
44.4153086° = 0.7751933733 rad (44° 24′ 55″)
Angle B
57.12165044° = 0.9969608743 rad (57° 7′ 18″)
Angle C
78.46304097° = 1.369438406 rad (78° 27′ 47″)
Area
14.69693846
Perimeter
18
Semiperimeter
9
Heights
hₐ = 5.878775383, h_b = 4.898979486, h_c = 4.199125273
Medians
mₐ = 6.020797289, m_b = 5.291502622, m_c = 4.272001873
Inradius
1.632993162
Circumradius
3.572172542
Vertices (A at the origin, B on the x-axis)
A (0, 0), B (7, 0), C (4.285714286, 4.199125273)
Centroid
(3.761904762, 1.399708424)
Incentre
(4, 1.632993162)
Circumcentre
(3.5, 0.7144345083)

The triangle's area is 14.69693846.

Show the working
  1. Three sides: each angle from the law of cosines, cos A = (b² + c² − a²) ÷ 2bc
  2. Area = √(s(s − a)(s − b)(s − c)) = 14.69693846

Two sides and the angle between (SAS)

Enter sides a and b and the angle C between them.

Opposite angle A.
Opposite angle B.
Opposite side c.
Degrees or radians.
Result
Area of the triangle
26.47986102
Type
obtuse scalene
Side a
8
Side b
11
Side c
6.666344593
Angle A
46.23748662° = 0.8069963794 rad (46° 14′ 15″)
Angle B
96.76251338° = 1.688824451 rad (96° 45′ 45″)
Angle C
37° = 0.6457718232 rad = 37π/180 (37° 0′ 0″)
Area
26.47986102
Perimeter
25.66634459
Semiperimeter
12.8331723
Heights
hₐ = 6.619965255, h_b = 4.814520185, h_c = 7.944342105
Medians
mₐ = 8.168235741, m_b = 4.895924337, m_c = 9.021638567
Inradius
2.063391686
Circumradius
5.538532885
Vertices (A at the origin, B on the x-axis)
A (0, 0), B (6.666344593, 0), C (7.608378836, 7.944342105)
Centroid
(4.758241143, 2.648114035)
Incentre
(4.833172296, 2.063391686)
Circumcentre
(3.333172296, 4.423269036)

The triangle's area is 26.47986102.

Show the working
  1. Two sides and the angle between them: the third side from the law of cosines, a² = b² + c² − 2bc cos A
  2. Area = √(s(s − a)(s − b)(s − c)) = 26.47986102

Two sides and a non-included angle (SSA)

Enter sides a and b and angle A (opposite a).

Opposite angle A.
Opposite angle B.
Opposite side a.
Degrees or radians.
Result
Area of the triangle
37.22368524
Type
acute scalene
Side a
10
Side b
8
Side c
10.26794809
Angle A
65° = 1.134464014 rad = 13π/36 (65° 0′ 0″)
Angle B
46.47269373° = 0.8111015178 rad (46° 28′ 22″)
Angle C
68.52730627° = 1.196027122 rad (68° 31′ 38″)
Area
37.22368524
Perimeter
28.26794809
Semiperimeter
14.13397404
Heights
hₐ = 7.444737048, h_b = 9.305921311, h_c = 7.250462296
Medians
mₐ = 7.727572645, m_b = 9.312109266, m_c = 7.459377354
Inradius
2.633631923
Circumradius
5.516889595
Vertices (A at the origin, B on the x-axis)
A (0, 0), B (10.26794809, 0), C (3.380946094, 7.250462296)
Centroid
(4.549631395, 2.416820765)
Incentre
(4.133974045, 2.633631923)
Circumcentre
(5.133974045, 2.019500262)

The triangle's area is 37.22368524.

Show the working
  1. A side and its opposite angle are known: the rest from the law of sines, a ÷ sin A = b ÷ sin B = c ÷ sin C
  2. Area = √(s(s − a)(s − b)(s − c)) = 37.22368524

Two angles and the side between (ASA)

Enter angles A and B and the side c between them.

Opposite side a.
Opposite side b.
Opposite angle C.
Degrees or radians.
Result
Area of the triangle
31.69872981
Type
acute scalene
Side a
7.320508076
Side b
8.965754722
Side c
10
Angle A
45° = 0.7853981634 rad = π/4 (45° 0′ 0″)
Angle B
60° = 1.047197551 rad = π/3 (60° 0′ 0″)
Angle C
75° = 1.308996939 rad = 5π/12 (75° 0′ 0″)
Area
31.69872981
Perimeter
26.2862628
Semiperimeter
13.1431314
Heights
hₐ = 8.660254038, h_b = 7.071067812, h_c = 6.339745962
Medians
mₐ = 8.763271036, m_b = 7.529855896, m_c = 6.479760652
Inradius
2.411809549
Circumradius
5.176380902
Vertices (A at the origin, B on the x-axis)
A (0, 0), B (10, 0), C (6.339745962, 6.339745962)
Centroid
(5.446581987, 2.113248654)
Incentre
(5.822623323, 2.411809549)
Circumcentre
(5, 1.339745962)

The triangle's area is 31.69872981.

Show the working
  1. A side and its opposite angle are known: the rest from the law of sines, a ÷ sin A = b ÷ sin B = c ÷ sin C
  2. Area = √(s(s − a)(s − b)(s − c)) = 31.69872981

Two angles and a non-included side (AAS)

Enter angles A and B and side a (opposite A).

Opposite side a.
Opposite side b.
Opposite angle A.
Degrees or radians.
Result
Area of the triangle
59.15063509
Type
acute scalene
Side a
10
Side b
12.24744871
Side c
13.66025404
Angle A
45° = 0.7853981634 rad = π/4 (45° 0′ 0″)
Angle B
60° = 1.047197551 rad = π/3 (60° 0′ 0″)
Angle C
75° = 1.308996939 rad = 5π/12 (75° 0′ 0″)
Area
59.15063509
Perimeter
35.90770275
Semiperimeter
17.95385138
Heights
hₐ = 11.83012702, h_b = 9.659258263, h_c = 8.660254038
Medians
mₐ = 11.97085085, m_b = 10.28597444, m_c = 8.851517661
Inradius
3.294593113
Circumradius
7.071067812
Vertices (A at the origin, B on the x-axis)
A (0, 0), B (13.66025404, 0), C (8.660254038, 8.660254038)
Centroid
(7.440169359, 2.886751346)
Incentre
(7.953851376, 3.294593113)
Circumcentre
(6.830127019, 1.830127019)

The triangle's area is 59.15063509.

Show the working
  1. A side and its opposite angle are known: the rest from the law of sines, a ÷ sin A = b ÷ sin B = c ÷ sin C
  2. Area = √(s(s − a)(s − b)(s − c)) = 59.15063509

How to use it

Enter the base and height. Enter the three sides. Enter sides a and b and the angle C between them. Enter sides a and b and angle A (opposite a). Enter angles A and B and the side c between them. Enter angles A and B and side a (opposite A).

Enter the values you know (decimals, fractions, surds such as 2√5, or angles such as π/3 in radians). Show the working gives the rule used at each step.

Key facts

A = ½ b h = ½ ab sin C = √(s(s − a)(s − b)(s − c))

Choosing a method

Use base × height when you have a height; Heron's formula with three sides; ½ ab sin C with two sides and the angle between them.

Questions

What is the area with base 10 and height 6?

30.

And with sides 8 and 11 at 37°?

≈ 26.47986102.

Reviewed by RK Calculator Team. Updated 2026-09-26.

Formulas

A = ½ b h = ½ ab sin C = √(s(s − a)(s − b)(s − c))

Sources

Limitations

  • Angles can be typed in degrees or radians; radians may be written with π (π/3, 2pi/3).

Formula version 0.1.0Reviewed