Free · Triangle calculators 🔺

Equilateral Triangle Side, Altitude and Circle Radii

Calculate equilateral triangle side, altitude and circle radii with retained unit controls, positive geometric roots and explicit inverse-branch assumptions.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Worked inputs Side (a) = 4 give Height (h) = 3.4641016, Area = 6.9282032, Perimeter = 12, Circumcircle radius = 2.3094011, Incircle radius = 1.1547005. Values use the initial displayed units.

h = a√3/2; A = a²√3/4; P = 3a; R = a√3/3; r = a√3/6

Worked example

Enter these known values and leave the other values blank.

Side (a)
4 cm
Height (h)
3.464 cm
Area
6.93 cm²
Perimeter
12 cm
Circumcircle radius
2.31 cm
Incircle radius
1.155 cm

Assumptions and limitations

  • All three sides are equal and all angles are 60°. The altitude is perpendicular to the opposite side; the circumradius is twice the inradius.
  • Lengths and areas are converted before calculation. Clear an unknown measurement instead of supplying conflicting dimensions.
  • Arithmetic uses 64 significant digits and full-precision π. Display rounding and measurement uncertainty are separate from the underlying arithmetic.

Common questions

Which measurements and inverse branch does this model use?

All three sides are equal and all angles are 60°. The altitude is perpendicular to the opposite side; the circumradius is twice the inradius.

How are the inscribed and circumscribed circle radii related?

The circumcircle radius is twice the incircle radius. Both circles share the centroid, and the altitude is three times the incircle radius.

References

The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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