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Impact Angle from Ellipse Width & Length

Estimate an impact angle from the short and long axes of an ideal elliptical mark, or solve an axis from a supplied angle.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A mark 1 cm wide and 2 cm long has width-to-length ratio 0.5, giving a modeled impact angle of arcsin(0.5) = 30°.

Modeled angle = arcsin(short-axis width / long-axis length)

Worked example

Enter these known values and leave the other values blank.

Short-axis width
1 cm
Long-axis length
2 cm
Modeled impact angle
30 deg

Assumptions and limitations

  • The shape is treated as an ideal ellipse formed under the geometric model. The width and length must be positive, and width cannot exceed length.
  • Measure the main elliptical body consistently. Tails, spines, surface texture, spreading and measurement uncertainty can affect a real mark.
  • The resulting angle lies above 0° through 90°. Equal axes correspond to 90° in this model.
  • This is a geometric estimate from two dimensions. It does not identify a source, event sequence, cause or three-dimensional point of origin.

Common questions

What does a circular mark give?

Equal width and length give a ratio of one, and the modeled angle is 90°.

Can I enter millimeters for one dimension and centimeters for the other?

Yes. Select the appropriate unit for each field; both are converted to a common length basis before forming the ratio.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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