Plane geometry measures a two-dimensional shape’s interior, boundary, diagonals, or defining side relationships.
Use it to solve a measurement relationship with every length in one consistent unit.
The relationship
Write the rule before calculating
Perimeter is the sum of all side lengths.
See the structure
What the calculation is doing
lengtharea insideboundary outsidePerimeter is the sum of all side lengths.
Worked interpretation
Read the result in context
Enter the example values shown in the fields to verify the stated relationship.
Interpret with care
Important boundary
Area and perimeter are different dimensions: area uses square units while a boundary uses ordinary length units.
Use the Mathematics collection to move between connected concepts without duplicating the calculation.
Understand the subject
What is perimeter?
Perimeter is the total length of a closed shape’s boundary.
Use it for borders, fencing, trim, paths, or any task concerned with distance around rather than space inside.
The relationship
The defining equation
P = s₁+s₂+⋯+sₙ
Each sᵢ is one consecutive side length around the boundary.
See the structure
Walk once around the edge
3434Trace and add the outer boundary once
Worked example
Rectangle 3 by 4
P=3+4+3+4=14 units
Interpret with care
What the result does—and does not—mean
Shared internal edges are not part of an outer perimeter. Curved boundaries require arc or circumference formulas.
Quick guide
How to use this calculator
Enter values using the notation shown beside each field.
Choose a calculation mode when the tool offers more than one interpretation.
Read the primary answer first, then inspect the supporting details.
Calculation method
Apply the stated definition
Perimeter is the sum of all side lengths.
The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.
Worked example
Worked example
Enter the example values shown in the fields to verify the stated relationship.
Perimeter is the sum of all side lengths.
Supported inputs
Precision and limits
Finite, bounded input
Numeric inputs use finite JavaScript floating-point values with magnitude limits. Results are normally displayed to 12 significant digits; outputs labelled approximate are not exact identities.
Notation
Lengths are unit-neutral but must use one consistent unit throughout a calculation. Angles are entered in degrees where labelled.
