Calculator
Example data table
| Example | Length | Width | W/L | Angle (deg) |
|---|---|---|---|---|
| Sample A | 14.0 | 7.0 | 0.500 | 30.0° |
| Sample B | 18.5 | 9.2 | 0.497 | 29.8° |
| Sample C | 10.0 | 3.0 | 0.300 | 17.5° |
Example angles are rounded and assume clean elliptical stains on a flat surface.
Formula used
When a droplet strikes a flat surface at an angle, the stain can appear elliptical. The impact angle θ is estimated from the stain’s minor and major axes:
θ = arcsin( W / L )
- L = stain length (major axis)
- W = stain width (minor axis)
- θ = impact angle (0° to 90°)
How to use this calculator
- Measure the stain’s longest axis as Length.
- Measure the shortest axis as Width.
- Enter one or more stains to compare consistency.
- Optionally add measurement uncertainty to see a range.
- Press Calculate, then export CSV or PDF if needed.
FAQs
1) Why is arcsin(width/length) used?
For an ideal elliptical stain, the minor-to-major axis ratio approximates sin(θ), where θ is the impact angle. Taking arcsin estimates θ.
2) What if the stain is not a clean ellipse?
Irregular edges, spines, or overlapping drops can distort axes. Use only well-formed stains, take several measurements, and treat results as estimates.
3) Does the unit matter?
No. The formula uses a ratio, so any consistent unit works. Units only affect how values are displayed and recorded in exports.
4) What happens if width is larger than length?
That usually means the axes were swapped. The calculator will swap them and add a warning so the ratio stays within valid limits.
5) Why enter multiple stains?
Multiple stains help reduce random measurement error and highlight outliers. The calculator shows average, median, and sample standard deviation for quick comparison.
6) How is the uncertainty range calculated?
A conservative ± value is applied to both length and width. The smallest plausible ratio gives a minimum angle, and the largest plausible ratio gives a maximum angle.
7) Can this determine direction of travel or origin?
No. This tool estimates only the impact angle from axes. Direction and area-of-origin require additional measurements, scene context, and validated methods.
8) Is this suitable for court conclusions?
It is a calculation aid, not an interpretation engine. Use validated protocols, document measurements, and consult qualified experts for formal reporting.