From a side
Side a
A = na²/[4 tan(π/n)]; P = na
Open calculator ↗GEOMETRY, ONE FIGURE AT A TIMERegular pentagon.
Regular pentagon.
Understand every measure.
Five equal sides and a golden connection. Four free tools, clear formulas and a little discovery along the way.
Find your calculator ↗FIGURE 132D / REFERENCE DRAWING
REGULAR PENTAGONNOT TO SCALE
THE CALCULATOR DESK
Start with what you know.
4 calculators available
From circumradius
Circumradius R
a = 2R sin(π/n)
Open calculator ↗From the apothem
Apothem r
a = 2r tan(π/n)
Open calculator ↗From area
Area A
a = √[4A tan(π/n)/n]
Open calculator ↗MEET THE FIGURE
A regular pentagon, explained.
A regular pentagon has five equal sides and five equal interior angles. An arbitrary five-sided polygon does not satisfy the same side-only formulas. All vertices lie on a common circumcircle.
Understand the properties ↗LOOK A LITTLE CLOSER
More than a formula.
Its diagonal-to-side ratio is the golden ratio.
The apothem reaches a side midpoint; the circumradius reaches a vertex. They are different lengths.
Explore three geometry facts ↗These tools use ideal Euclidean geometry. Every input must use the same unit. Numerical results are rounded and do not replace measurement, specialist design or safety checks. See worked examples.