How to calculate radius

How to calculate radius

Radius, is the parameter which precisely determines the sizes of a circle or the sphere - knowledge its one enough for creation of such geometrical figures. Radius is connected by rather simple ratios with other characteristics of roundish geometrical figures - perimeter, the area, volume, surface area, etc. It allows to find simple calculations radius according to indirect data.


1. If it is required to calculate the radius (R) of a circle which perimeter (P) is given in initial conditions, you divide circle length - perimeter - into the doubled Pi's number: R = P/(2*π).

2. The area (S) of the plane, a limited circle, can be expressed through the radius (R) and number by Pi too. If it is known, take a square root from a ratio between the area and Pi's number: R = √ (S/π).

3. Knowing length of an arch (L), i.e. part of perimeter of a circle, and the central corner corresponding to it (α) the radius of a circle (R) it is possible to calculate too. If the central corner is expressed in radians, just divide into it arch length: R = L/α. If the corner is given in degrees, the formula considerably will become complicated. Multiply arch length by 360 °, and you divide the received result into the doubled work of number of Pi at a size of the central corner in degrees: R = 360*L / (2*π*α).

4. It is possible to express radius (R) and through length of the chord (m) connecting extreme points of an arch if the corner size measured in degrees is known (α) which forms this sector of a circle. Divide a half of length of a chord into a sine of a half of size of a corner: R = m/(2*sin(α/2)).

5. If it is necessary to calculate the radius (R) of the sphere in which the known volume of space (V) is concluded, it is necessary to calculate a cubic root. As a radicand use the trebled volume divided into four numbers of Pi: R =³ √ (3*V / (4*π).

6. Knowledge of surface area of the sphere (S) will allow to calculate the radius of a sphere (R) too. For this purpose take a square root from a ratio between the area and Pi's number increased four times: R = √ (S / (4*π).

7. Knowing not all area of the sphere, but only an area (s) of its site - a segment - assigned altitude (H), it is possible to count the radius (R) of a volume figure too. Divide a half of the area of a segment into the work of height on Pi's number: R = √ (s / (2*π*H)).

8. Calculation of radius (R) on the known diameter (D) figure will be the simplest. Halve this size and receive required value both for a circle, and for the sphere: R = D/2.

Author: «MirrorInfo» Dream Team