Octagon Area CalculatorFree online math calculator — instant results, no sign-up
Calculate the area of a regular octagon.
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About the Octagon Area Calculator
The Octagon Area Calculator finds the area of a regular octagon from the length of one side. It assumes all eight sides are equal and all eight interior angles are equal. With the default side length of 5, it returns an area of 120.7106781187 square units.
- Side length
- The length of any one of the regular octagon’s eight equal sides, entered in a consistent linear unit such as centimeters, meters, or inches; the default is 5.
Formula and method
A = 2(1 + √2)s²; for s = 5, A = 2(1 + √2) × 5² ≈ 120.7106781187.
- AArea of the regular octagon, expressed in square units.
- sLength of one of the octagon’s eight equal sides, expressed in linear units.
Square the side length, then multiply by the regular-octagon factor 2(1 + √2). With the default input, 5² = 25, so the calculation is 2(1 + √2) × 25 = 50(1 + √2), giving the displayed result of 120.7106781187.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Side length5
Results
- Result120.7106781187
How to use the Octagon Area Calculator
- 1Confirm that the shape is a regular octagon with eight equal sides and eight equal interior angles.
- 2Identify the length of one side, rather than the distance across the octagon.
- 3Enter that measurement in Side length, or leave the default value of 5.
- 4Calculate the area using A = 2(1 + √2)s².
- 5Read the Result as an area in square units; for Side length = 5, Result = 120.7106781187.
Reading your result
The Result row reports the area enclosed by the regular octagon. For the default side length of 5, the result is 120.7106781187 square units. If the side length is measured in centimeters, the result is in square centimeters; if it is measured in meters, the result is in square meters. The displayed decimal is an approximation of the exact area 50(1 + √2).
Limitations
This formula applies only to regular octagons, whose eight equal interior angles are each 135°. A single side length is not enough to determine the area of an irregular octagon, even if all its sides are equal. Enter a positive side length for a nondegenerate octagon, and do not substitute an across-flats or corner-to-corner measurement. Results inherit any measurement uncertainty in the input, and the displayed decimal precision does not imply equivalent measurement accuracy.
Common questions
Can I use this calculator for an octagon with unequal sides?+
No. The formula A = 2(1 + √2)s² requires a regular octagon. An irregular octagon needs additional dimensions or vertex coordinates to determine its area.
Is Side length the distance across the octagon?+
No. Side length is the length of one boundary edge between adjacent vertices. The distance between opposite sides or opposite vertices is a different measurement and cannot be entered directly.
Why does a side length of 5 produce 120.7106781187 rather than an exact terminating decimal?+
The exact area is 50(1 + √2). Because √2 is irrational, the decimal expansion does not terminate; 120.7106781187 is the rounded displayed value.
How does changing the side length affect the octagon’s area?+
The area is proportional to the square of the side length. Doubling every side of a regular octagon makes its area four times as large, while preserving its shape.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.