Inputs
Result
Enter a value and click Calculate Perimeter to see the result.
How it works
This tool assumes a regular pentagon (all sides and angles equal). Depending on the input provided:
- From side:
P = 5s - From apothem:
s = 2a\\tan(\\pi/5), thenP = 5s - From circumradius:
s = 2R\\sin(\\pi/5), thenP = 5s
Units carry through unchanged (input and perimeter share the same unit).
Step-by-step solution
Your detailed steps will appear here after calculation.
FAQs
- 1) What is the formula for the perimeter of a regular pentagon?
- The perimeter is five times the side length:
P = 5s. If you do not have the side, you can compute it from the apothem or circumradius using trigonometric relations for a regular polygon. - 2) Can I calculate the perimeter if I know only the apothem?
- Yes. Use
s = 2a\\tan(\\pi/5)to find the side from the apothema, then multiply by five. - 3) How do I use the circumradius to get the perimeter?
- Use
s = 2R\\sin(\\pi/5)to obtain the side from the circumradiusR, then the perimeter isP = 5s. - 4) Which unit should I choose?
- Select the unit that matches your measurement (mm, cm, m, in, ft). The result is presented in the same unit; no conversion is applied.
- 5) What is the difference between apothem and circumradius?
- The apothem is the distance from the center to the midpoint of a side, while the circumradius is the distance from the center to a vertex.
- 6) How many decimals should I use?
- Choose the precision that matches your application. Engineering drawings might need more decimals, whereas quick estimates may use fewer.
- 7) Does this work for non-regular pentagons?
- No. The formulas here assume equal sides and angles. For irregular shapes, you must sum the lengths of all five sides directly.