Free · Mathematics models
Perimeter of Plane Shapes
Find boundary length for circles, sectors, triangles, quadrilaterals, annuli and regular polygons with all captured entry branches.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
A circle of radius 1 centimeter has circumference about 6.283185 centimeters.
Perimeter adds straight and curved boundary lengths; the ellipse branch uses Ramanujan’s first approximation.
Worked example
Enter these known values and leave the other values blank.
- Radius (r)
- 1 cm
- Circle circumference
- 6.283 cm
Assumptions and limitations
- All lengths are positive and entered geometry must be realizable. Regular polygon side count is an exact integer of at least three. The annulus includes both circular boundaries. The semicircle branch uses plain numerical lengths in one consistent chosen unit.
- Triangle, rhombus and parallelogram entry branches retain their own reconstruction equations. Ellipse perimeter is an approximation, not an exact elliptic integral.
- Self-intersecting boundaries, spherical geometry and measurement uncertainty are omitted.
- Clear the unknown numerical field before using a supported inverse; selection controls retain their captured branches.
Common questions
What assumptions matter for this model?
All lengths are positive and entered geometry must be realizable. Regular polygon side count is an exact integer of at least three. The annulus includes both circular boundaries. The semicircle branch uses plain numerical lengths in one consistent chosen unit.
What does this model leave out?
Self-intersecting boundaries, spherical geometry and measurement uncertainty are omitted.
References
- OpenStax: law of cosines and sine rule
- NIST: mathematical constants and ellipse approximation context
- Calculation definition and unit reference
Model requirements: Regular polygons require an exact whole side count of at least three. Authored accessible explanations preserve each captured diagram mode and its geometric relationships. Use the mathematical pi constant for triangle angle sums instead of the captured 3.1415, preserving all reconstruction branches.