How this calculator works
Splitting the triangle down an altitude makes two 30°-60°-90° triangles. Their proportions connect the side and height. The centre lies one-third of the height above the base, giving an inradius of h/3 and a circumradius of 2h/3. Every input mode first recovers the side length, then calculates the other measurements.
Formula
h = √3 a/2; K = √3 a²/4; P = 3a; R = a/√3; r = a/(2√3); each angle = 60°.
Worked example
A side of 2 m gives height √3 m, area √3 m² and perimeter 6 m. A perimeter of 12 cm gives a side of 4 cm and area 4√3 cm².
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Frequently asked questions
Are the incircle and circumcircle concentric?
Yes. Their common centre is also the centroid, and the circumradius is twice the inradius.
Can I enter area instead of a length?
Yes. Select area and enter a positive square-unit value. The side grows with the square root of the area.
Does zero make a triangle?
No. A zero measurement collapses the figure, so all size inputs must be positive.