Regular Polygon Miter Frame Calculator
Calculate matching inside and outside piece lengths for a regular frame with a fixed perpendicular border width.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Offset every side outward by the same border width. Use half the exterior turn as the miter angle from a square crosscut, then extend both piece ends using the tangent relation.
Miter from square=180°/N; outside side=inside side+2×border width×tan(π/N)
Worked example
A square frame with 300 mm inner side and 40 mm border has 45° end miters and 380 mm outside long-point piece lengths. Four such pieces sum to 1520 mm before cutting allowances.
Assumptions and input details
Regular coplanar closed frame, equal straight pieces and constant-width borders. Miter is measured from a square crosscut, not from the long edge. Outside long-point sums are not an optimized stock cutting plan and exclude saw kerf, defects and joint gaps. No bevel, compound corner or construction-tolerance model.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Find a regular polygon’s area, perimeter, apothem, circumradius and angles from side count and length. Choose global length units and compare dimensions.
Find a minimum identical-stock allocation under an explicit per-piece kerf reservation and end-trim convention.
Calculate neutral-axis bend allowance and flat length from entered outside flange dimensions and K factor.
Reserved advertising space.