# Pentagon Measurement Calculator

The side length, height, diagonal, center-to-side, center-to-vertex, and area of a regular pentagon are all interrelated. If you know one of these dimensions, you can compute the others.

For example, suppose the side length is **s**. If the height is **h**, the diagonal between non-adjacent vertices **d**, the distance from the side to the center **k**, the distance from the vertex to the center **r**, the area **a**, and the perimeter **p**, then you can find each measure with the following formulas:

r = s/[2*sin(π/5)]

h = r[1+cos(π/5)]

k = h - r

c = h/cos(π/10)

a = 2.5sk

p = 5s

Here, sin and cos are in radians, not degrees. (For conversion purposes, π/5 radians is 36°, and π/10 radians is 18°.)

You can perform these computations using a hand calculator, our online scientific calculator, or the convenient pentagonal measurement calculator at left. All results are accurate within 5 decimal places.

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