BIZOMAT MAKEOS · Geometry
Ellipse Area and Perimeter
What area, perimeter and eccentricity does this ellipse have?
Area, perimeter (Ramanujan’s second approximation) and eccentricity of an ellipse from its two axes.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Major axis (full length) | mm | Longest overall dimension from the drawing. |
| Minor axis (full width) | mm | Shortest overall dimension, at right angles to the major axis. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Major axis (full length)
- What it is
- The full length of the ellipse along its longest direction, from one end to the other through the centre.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the full length, not the semi-axis; the tool halves it. If the two values are swapped, the larger one is used as the major axis.
What this means: Minor axis (full width)
- What it is
- The full width of the ellipse along its shortest direction, at right angles to the major axis through the centre.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the full width, not the semi-axis.
Method and formulas
- With semi-axes a and b: area = πab.
- Perimeter ≈ π(a + b)(1 + 3λ ÷ (10 + √(4 − 3λ))), λ = ((a − b) ÷ (a + b))².
- Eccentricity e = √(1 − b² ÷ a²); focal distance = a × e.
- Example: 400 × 300 mm gives an area of 94,248 mm² and a perimeter of 1,105.2 mm.
Limitations
- The perimeter formula is an approximation; its error is negligible for engineering ellipses.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate gasket or seal length for elliptical manways
- Area of elliptical openings and cut-outs
- Lay out elliptical heads
Who it is for
- Design engineers
- Toolmakers
- Estimators
What you get
- Area
- Perimeter
- Eccentricity
- Focal distance from centre
Interpreting the result
- Add seam allowance or overlap when cutting seals or strips to the perimeter.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 48–50, 70–75. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Polygons, ellipses and inclined views
In Drafting Geometry by the Numbers
What it covers: Draw regular polygons by across-flats or across-corners size, construct the ellipses that circles become on inclined faces and oblique cuts, and estimate an ellipse's perimeter.
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