Perimeter Calculator
Calculate the boundary length of 12 common shapes, convert the result across practical length units, and export the complete calculation to a real Excel workbook.
Shape and measurements
Choose the geometric figure whose outer boundary you need.
Select the formula that matches the measurements you know.
Changing units converts the current length values without changing the physical shape.
Enter a positive finite length.
Enter a positive finite length.
Enter the required measurement.
Enter the required measurement.
Live result
Perimeter
70 m
The total distance around the rectangle.
In meters
70 m
In feet
229.6588 ft
Boundary terms
4
P = 2 × (length + width)
Rectangle perimeter is 70 meters.
Measurement summary
| Measurement | Value | Role in the formula |
|---|---|---|
| Length | 20 m | One of two repeated rectangle sides |
| Width | 15 m | The other repeated rectangle side |
All lengths are converted internally to meters, calculated at full precision, and then displayed in your selected unit. Angles and side counts remain dimensionless controls.
How to use this perimeter calculator
What this calculator does
This calculator estimates the total boundary length of a closed two-dimensional shape. It supports a square, rectangle, triangle, circle, circle sector, ellipse, trapezoid, parallelogram, rhombus, kite, annulus, and regular polygon. For straight-sided figures, perimeter is the sum of the outside edges. For curved figures, the calculator applies a circumference or arc-length formula. The result is an exact identity for most supported shapes when the measurements are exact; the ellipse result uses a well-known Ramanujan approximation, so it is extremely useful but not a symbolic exact circumference.
When to use it
Use the calculator to estimate fencing around a plot, trim around a room, edging around a garden bed, the travel distance around a wheel, or the material needed along the boundary of a fabricated part. It is also useful for checking geometry homework, comparing shapes measured in different units, and documenting a calculation in an Excel workbook. Perimeter does not determine area by itself for most shapes, so do not treat the boundary length as a surface-area estimate.
How to calculate
- The calculator opens with a ready-to-use rectangle example: Length 20 m and Width 15 m. Its perimeter is 70 m, and the Download Excel button is immediately available.
- Choose a value in Shape. Then use Known measurements when the figure offers more than one valid formula, such as a triangle, parallelogram, or rhombus.
- Select the Length unit. When you switch units, the current length entries are converted so the physical dimensions remain unchanged.
- Replace the measurement values shown for the active formula. The result, unit conversions, formula, and measurement table update live.
- Select Download Excel to export the current validated model. Select Reset to clear the demonstration and all calculation data; Excel export is then disabled until a complete valid state is entered again.
Input guide
Shape is required and determines the formula. Known measurements is required when multiple data sets can define the same perimeter. Length unit is required and accepts millimeters, centimeters, meters, kilometers, inches, feet, or yards. All measurement fields use a strict decimal format: examples include 12, 12.5, or 1,250.75. Decimal commas such as 1,5 and scientific notation such as 1e3 are rejected to prevent ambiguous interpretation.
The adaptive measurement labels may include Side, Length, Width, Side a, Side b, Side c, Radius, Central angle, Semi-major axis, Semi-minor axis, Outer radius, Inner radius, Diagonal e, Diagonal f, Height, or Number of sides. Lengths must normally be greater than zero; the annulus inner radius may be zero but must be smaller than the outer radius. Angles are entered in degrees. A triangle included angle and a parallelogram angle must be greater than 0° and less than 180°; a sector angle may be up to 360°. A regular polygon needs a whole-number side count of at least 3. Common mistakes include entering diameter where radius is requested, full ellipse axes where semi-axes are requested, or three triangle sides that violate the triangle inequality.
Output guide
The header Shape, Unit, and Inputs used pills confirm the active figure, selected length unit, and number of supplied controls used by the formula. Perimeter is the primary result in the selected length unit. In meters and In feet are direct unit conversions of the same boundary length. Boundary terms reports the number of additive edge or curve terms represented by the selected formula; it is a descriptive count, not a unit conversion. Formula used identifies the active geometric relationship. The Measurement summary table lists each supplied or derived measurement, its current value, and its role in the formula. A zero result is not shown for an incomplete or invalid model. Very high results usually reflect large dimensions or a unit-selection mistake rather than a special geometric condition.
Worked example
The startup rectangle has a length of 20 m and a width of 15 m. A rectangle has two sides of each length, so P = 2 × (20 + 15) = 2 × 35 = 70 m. The same boundary is 229.6588 ft after conversion. The workbook records the typed inputs, selected unit, formula, perimeter in the chosen unit, and normalized meter and foot values.
Learn more
Perimeter is always expressed as a length, so consistent units are essential. The NIST guide to SI length units explains the meter and metric relationships used by the conversion engine. For curved boundaries, the Wolfram MathWorld circle reference provides the circumference relationship, while its ellipse reference discusses ellipse geometry and circumference approximations.
Formula notes and practical interpretation
For polygons, the conceptual rule is simple: add every outer side exactly once. Symmetry shortens the arithmetic. A square uses four equal sides, a rectangle has two equal pairs, and a kite has two adjacent pairs. A regular polygon multiplies one side length by the number of equal sides. Triangles require extra validation because any two sides must add to more than the third.
Curved figures require care about what belongs to the boundary. A full circle uses one circumference. A sector includes the curved arc plus two radii. An annulus has two circular boundaries, so both the outer and inner circumferences count. For an ellipse, the semi-major and semi-minor axes are radii from the center, not full widths. The calculator uses Ramanujan's first approximation, which is accurate for ordinary geometry and engineering estimates.
Common perimeter mistakes
- Using area units such as m² for a perimeter. Boundary length always uses linear units such as m, cm, or ft.
- Leaving out an inner boundary. Rings and openings may have more than one edge that needs material.
- Counting shared or internal lines. Perimeter normally follows only the exterior boundary of the selected figure.
- Rounding measurements too early. Keep source dimensions at useful precision and round only the final displayed result.
- Assuming equal perimeter means equal area. Different shapes can share the same boundary length and enclose very different areas.