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Triangle calculator

Solve a triangle from three known measurements. Find angles, heights, medians and circle centers.

Get started

  1. Enter three measurements, including at least one side.
  2. Select radians for inputs like π/2, or use degrees. In SSA, both an acute and a supplementary angle can give valid triangles.
  3. The coordinate table uses A at the origin and B on the positive x-axis. Export the selected table as CSV.

Example

Input

a = 7, b = 10, A = 30°

Expected result

Two solutions, with c about 13.55923 and 3.76127.

Try it

Good to know

The calculation runs in your browser. Use consistent units in fields with no explicit unit.

Calculation method

Use one length unit. Side a is opposite angle A, and likewise for b/B and c/C. Angles alone do not determine a size.

asin⁡A=bsin⁡B=csin⁡C,a2=b2+c2−2bccos⁡A\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C},\qquad a^2=b^2+c^2-2bc\cos A
Δ=s(s−a)(s−b)(s−c),s=a+b+c2,ha=2Δ/a\Delta=\sqrt{s(s-a)(s-b)(s-c)},\quad s=\tfrac{a+b+c}{2},\quad h_a=2\Delta/a
ma=122b2+2c2−a2,r=Δ/s,R=abc/(4Δ)m_a=\tfrac12\sqrt{2b^2+2c^2-a^2},\qquad r=\Delta/s,\qquad R=abc/(4\Delta)

Calculation mode

Known measurements
  • Side a
  • Side b
  • Side c
  • Angle A
  • Angle B
  • Angle C
  • Angle unit · Degrees / Radians
Three sides (SSS)
  • Side a
  • Side b
  • Side c
Two sides and included angle (SAS)
  • Side b
  • Side c
  • Angle A · °
Two angles and one side (ASA / AAS)
  • Angle A · °
  • Angle B · °
  • Known side · a / b / c
  • Side
Two sides and opposite angle (SSA)
  • Side a
  • Side b
  • Angle A · °
Right triangle legs
  • Side a
  • Side b