MasterTool

Triangle Calculator

Calculate triangle instantly in your browser.

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What this tool does

Calculate triangle instantly in your browser. Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.

How to use the Triangle Calculator

  1. Enter or select given.
  2. Enter or select side a.
  3. Enter or select side b.
  4. Enter or select side c.
  5. Enter or select angle a (degrees, opposite side a).
  6. Enter or select angle b (degrees, opposite side b).
  7. Read the calculated result; change any measurement to compare alternatives.

Formula

SSS uses the law of cosines for angles and Heron's formula for area. SAS completes the third side with the law of cosines. ASA/AAS first find the third angle (angles sum to 180°), then scale all sides with the law of sines. Area = ½·a·b·sin C.
mode
Given
a
Side a
b
Side b
c
Side c
angA
Angle A (degrees, opposite side a)
angB
Angle B (degrees, opposite side b)

Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.

Worked example

For triangle calculator, the following measurements illustrate the exact method: Given: sss; Side a: 3; Side b: 4; Side c: 5; Angle A (degrees, opposite side a): 60; Angle B (degrees, opposite side b): 60.

Inputs

  • GivenThree sides (SSS)
  • Side a3
  • Side b4
  • Side c5
  • Angle A (degrees, opposite side a)60
  • Angle B (degrees, opposite side b)60

Result

  • Side a3
  • Side b4
  • Side c5
  • Angle A (degrees)36.87
  • Angle B (degrees)53.13
  • Angle C (degrees)90
  • Area6
  • Perimeter12
  • Inradius1
  • Circumradius2.5

Results explained

Side a
Side a from the formula above. Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.
Side b
Side b from the formula above. Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.
Side c
Side c from the formula above. Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.
Angle A (degrees)
Angle A (degrees) from the formula above. Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.
Angle B (degrees)
Angle B (degrees) from the formula above. Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.
Angle C (degrees)
Angle C (degrees) from the formula above. Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.
Area
Area from the formula above. Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.
Perimeter
Perimeter from the formula above. Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.
Inradius
Inradius from the formula above. Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.
Circumradius
Circumradius from the formula above. Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.

Frequently asked questions

SSS uses the law of cosines for angles and Heron's formula for area. SAS completes the third side with the law of cosines. ASA/AAS first find the third angle (angles sum to 180°), then scale all sides with the law of sines. Area = ½·a·b·sin C.

Angles are in degrees and side a is always opposite angle A (standard notation). Ambiguous SSA input is not offered because it can describe two different triangles.

Where mathematically meaningful, yes. Fields specify permitted ranges and undefined operations display an error.

Exact integer calculations use safe integers; decimal calculations use browser floating point, so small rounding differences can occur.

All values remain in your browser and are never uploaded.