Calculator Inputs
Choose one known measurement. The calculator derives the remaining values instantly.
Example Data Table
These sample rows show how one input can produce the other regular octagon properties.
| Example | Known Type | Known Value | Side Length | Perimeter | Area |
|---|---|---|---|---|---|
| Example 1 | Side Length | 5 | 5 | 40 | 120.7107 |
| Example 2 | Perimeter | 64 | 8 | 64 | 309.0193 |
| Example 3 | Apothem | 12 | 9.9411 | 79.5285 | 476.5708 |
Formula Used
Core formulas from side length s
Perimeter: P = 8s
Area: A = 2(1 + √2)s²
Apothem: a = s / (2 tan(π/8))
Circumradius: R = s / (2 sin(π/8))
Flat-to-flat span: Df = 2a
Corner-to-corner span: Dc = 2R
Inverse formulas used by the calculator
From perimeter: s = P / 8
From area: s = √(A / (2(1 + √2)))
From apothem: s = 2a tan(π/8)
From circumradius: s = 2R sin(π/8)
From flat span: s = Df tan(π/8)
From corner span: s = Dc sin(π/8)
All linear outputs keep the same unit as the input. Area uses the square of that unit.
How to Use This Calculator
- Select the measurement you already know.
- Enter its value in the measurement field.
- Choose how many decimal places you want displayed.
- Press Calculate Octagon.
- Review the result panel shown above the form.
- Use the export buttons to save the result as CSV or PDF.
- Check the Plotly graph to visualize the octagon shape.
FAQs
1. What makes an octagon regular?
A regular octagon has eight equal sides and eight equal interior angles. This lets one measurement determine the remaining dimensions exactly.
2. Which input should I use first?
Use whichever measurement you already know. Side length is the most direct option, but perimeter, area, apothem, radii, and spans work too.
3. Are the units converted automatically?
No unit conversion is applied. If you enter centimeters, all linear outputs stay in centimeters and the area appears in square centimeters.
4. What is the apothem in a regular octagon?
The apothem is the perpendicular distance from the center to the midpoint of any side. It is also half of the flat-to-flat span.
5. What is the difference between flat span and corner span?
Flat span measures across opposite sides. Corner span measures across opposite vertices. Corner span is always larger for a regular octagon.
6. Can I use decimal values?
Yes. The calculator accepts decimal inputs and lets you choose the displayed precision, which is useful for design, drafting, and coursework.
7. Why does the area unit look different?
Area is two-dimensional, so it uses squared units. For example, a side entered in meters produces an area in square meters.
8. Is this useful for construction and layout work?
Yes. The side, span, diagonal, apothem, and perimeter outputs help with marking layouts, estimating material needs, and checking geometric consistency.