MasterTool

Law of Sines Calculator

Calculate law of sines instantly in your browser.

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What this tool does

Calculate law of sines instantly in your browser. Standard notation: side a is opposite angle A. This is the unambiguous ASA/AAS case — the ambiguous SSA case can yield two triangles and is not solved here.

How to use the Law of Sines Calculator

  1. Enter or select known side a.
  2. Enter or select angle a opposite side a (degrees).
  3. Enter or select angle b (degrees).
  4. Read the calculated result; change any measurement to compare alternatives.

Formula

a/sin A = b/sin B = c/sin C = 2R: knowing one side–angle pair sets the ratio, angle B then gives side b, and angle C = 180° − A − B gives side c.
a
Known side a
angA
Angle A opposite side a (degrees)
angB
Angle B (degrees)

Standard notation: side a is opposite angle A. This is the unambiguous ASA/AAS case — the ambiguous SSA case can yield two triangles and is not solved here.

Worked example

For law of sines calculator, the following measurements illustrate the exact method: Known side a: 10; Angle A opposite side a (degrees): 30; Angle B (degrees): 45.

Inputs

  • Known side a10
  • Angle A opposite side a (degrees)30
  • Angle B (degrees)45

Result

  • Side b14.14
  • Side c19.32
  • Angle C (degrees)105
  • Circumdiameter (2R)20
  • Area68.3

Results explained

Side b
Side b from the formula above. Standard notation: side a is opposite angle A. This is the unambiguous ASA/AAS case — the ambiguous SSA case can yield two triangles and is not solved here.
Side c
Side c from the formula above. Standard notation: side a is opposite angle A. This is the unambiguous ASA/AAS case — the ambiguous SSA case can yield two triangles and is not solved here.
Angle C (degrees)
Angle C (degrees) from the formula above. Standard notation: side a is opposite angle A. This is the unambiguous ASA/AAS case — the ambiguous SSA case can yield two triangles and is not solved here.
Circumdiameter (2R)
Circumdiameter (2R) from the formula above. Standard notation: side a is opposite angle A. This is the unambiguous ASA/AAS case — the ambiguous SSA case can yield two triangles and is not solved here.
Area
Area from the formula above. Standard notation: side a is opposite angle A. This is the unambiguous ASA/AAS case — the ambiguous SSA case can yield two triangles and is not solved here.

Frequently asked questions

a/sin A = b/sin B = c/sin C = 2R: knowing one side–angle pair sets the ratio, angle B then gives side b, and angle C = 180° − A − B gives side c.

Standard notation: side a is opposite angle A. This is the unambiguous ASA/AAS case — the ambiguous SSA case can yield two triangles and is not solved here.

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.