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Triangle Perimeter Calculator

Find a triangle's perimeter from three sides, two sides and the angle between, or a side and two angles.

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

Three sides

Enter the three sides.

Opposite angle A.
Opposite angle B.
Opposite angle C.
Result
Perimeter of the triangle
18
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 perimeter is 18.

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

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

Opposite angle A.
Opposite angle B.
Opposite side c.
Degrees or radians.
Result
Perimeter of the triangle
18.244998
Type
acute scalene
Side a
5
Side b
7
Side c
6.244997998
Angle A
43.89788625° = 0.7661626497 rad (43° 53′ 52″)
Angle B
76.10211375° = 1.328232453 rad (76° 6′ 8″)
Angle C
60° = 1.047197551 rad = π/3 (60° 0′ 0″)
Area
15.15544457
Perimeter
18.244998
Semiperimeter
9.122498999
Heights
hₐ = 6.062177826, h_b = 4.330127019, h_c = 4.853626717
Medians
mₐ = 6.144102864, m_b = 4.444097209, m_c = 5.220153254
Inradius
1.661325977
Circumradius
3.605551275
Vertices (A at the origin, B on the x-axis)
A (0, 0), B (6.244997998, 0), C (5.044036845, 4.853626717)
Centroid
(3.763011614, 1.617875572)
Incentre
(4.122498999, 1.661325977)
Circumcentre
(3.122498999, 1.802775638)

The triangle's perimeter is 18.244998.

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)) = 15.15544457

A side and two angles

Enter side a, its opposite angle A and angle B.

Opposite angle A.
Opposite side a.
Opposite side b.
Degrees or radians.
Result
Perimeter of the triangle
26.85757977
Type
acute scalene
Side a
8
Side b
9.044126999
Side c
9.813452775
Angle A
50° = 0.872664626 rad = 5π/18 (50° 0′ 0″)
Angle B
60° = 1.047197551 rad = π/3 (60° 0′ 0″)
Angle C
70° = 1.221730476 rad = 7π/18 (70° 0′ 0″)
Area
33.99479761
Perimeter
26.85757977
Semiperimeter
13.42878989
Heights
hₐ = 8.498699402, h_b = 7.517540966, h_c = 6.92820323
Medians
mₐ = 8.546931863, m_b = 7.72676319, m_c = 6.987285077
Inradius
2.531486299
Circumradius
5.221629157
Vertices (A at the origin, B on the x-axis)
A (0, 0), B (9.813452775, 0), C (5.813452775, 6.92820323)
Centroid
(5.208968517, 2.309401077)
Incentre
(5.428789887, 2.531486299)
Circumcentre
(4.906726388, 1.785902353)

The triangle's perimeter is 26.85757977.

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)) = 33.99479761

How to use it

Enter the three sides. Enter sides a and b and the angle C between them. Enter side a, its opposite angle A and angle B.

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

P = a + b + c

Finding the missing sides

With two sides and the angle between them, the law of cosines gives the third; with a side and two angles, the law of sines gives the others.

Questions

What is the perimeter of a 5-6-7 triangle?

18.

With sides 5 and 7 at 60°?

12 + √39 ≈ 18.244998.

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

Formulas

P = a + b + 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