When a falling drop of blood hits a surface straight on, it leaves a nearly circular stain. The more oblique the impact, the more the stain is stretched into an ellipse with a tail pointing in the direction of travel. Bloodstain pattern analysts use this to reconstruct events: the ratio of the stain’s width (minor axis) to its length (major axis) equals the sine of the impact angle, a relationship confirmed by drop experiments since the 1970s.
Measure the width across the widest part of the ellipse and the length along its long axis, leaving out the tail and any satellite spatter. The calculator returns the impact angle in degrees and radians and the W/L ratio. If you also enter the horizontal distance from the stain to the area of convergence – the point where the stains’ flight paths cross on the surface – it estimates how high above the surface the blood source was, using the tangent method. Investigators combine several well-formed stains, since a single stain carries measurement error of a few degrees.
The same geometry applies to any liquid drop, so the calculator is equally useful for classroom experiments with fake blood or coloured water.
How to use the Angle of Impact Calculator
- Width of the stain (minor axis)
- Length of the stain (major axis, without the tail)
- Distance to the area of convergence (optional)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the stain’s width and length in any unit (both in the same scale), and optionally the distance to the area of convergence. The calculator takes the arcsine of W/L and multiplies the distance by the tangent of the angle.
Worked example
A stain measures 6 mm wide and 11 mm long. W/L = 0.5455 and arcsin(0.5455) = 33.1°, a moderately oblique impact. The area of convergence lies 80 cm away, so the source was at most about 80 × tan 33.1° = 52.1 cm above the surface. A second stain 1.8 cm long and 0.9 cm wide gives exactly 30°; at 120 cm from convergence it points to 120 × tan 30° = 69.3 cm.
Stain shape by angle
| Angle | W/L ratio | Typical appearance |
|---|---|---|
| 90° | 1.00 | Round, spines all around |
| 60° | 0.87 | Slightly oval |
| 30° | 0.50 | Ellipse twice as long as wide |
| 15° | 0.26 | Long ellipse with clear tail |
| 10° | 0.17 | Very elongated, exclamation-mark shape |
Inputs explained
| Field | What to enter |
|---|---|
| Width of the stain (minor axis) | Units: mm, cm, in |
| Length of the stain (major axis, without the tail) | Units: mm, cm, in |
| Distance to the area of convergence (optional) | Units: cm, m, in, ft |
What each result means
- Angle in radians = [Angle in radians]([Angle of impact])
- Width-to-length ratio = [Width of the stain (minor axis)]÷[Length of the stain (major axis, without the tail)]
- Estimated height of the source above the surface = [Distance to the area of convergence (optional)]×tan([Angle in radians]([Angle of impact]))
Formula
Angle of impact α = arcsin(W ÷ L)
Height of origin ≈ d × tan α (d = distance from the stain to the area of convergence)
Worked example
Inputs — Width of the stain (minor axis): 6 mm; Length of the stain (major axis, without the tail): 11 mm; Distance to the area of convergence (optional): 80 cm.
Results — Angle of impact = 33.1 °; Angle in radians = 0.5769; Width-to-length ratio = 0.545; Estimated height of the source above the surface = 52.1 cm; Impact type = Oblique – clear tail expected.
Key terms
- Angle of impact
- Angle at which a blood drop strikes a surface, from 0° (glancing) to 90° (perpendicular).
- Area of convergence
- Point on the surface where lines drawn back along the stains' directions intersect.
- Area of origin
- 3-D location of the blood source, found from the area of convergence and the impact angles.
- Directionality
- The direction a drop was travelling, shown by the stain's tail or narrower end.
Frequently asked questions
What is the angle of impact of a bloodstain?
The acute angle between the drop's direction of travel and the surface it hit. A round stain means about 90°; a long, narrow stain means a shallow angle.
How do you calculate the angle of impact?
Divide the stain's width by its length and take the arcsine: a 1 cm wide, 2 cm long stain gives arcsin(0.5) = 30°.
Should I include the tail when measuring length?
No. Measure the ellipse only – the tail and satellite drops would make the angle look smaller than it really is.
How is the height of the blood source found?
Multiply the horizontal distance from the stain to the area of convergence by tan α. A 33.1° stain 80 cm from convergence points to a source about 52 cm high.
How accurate is the formula?
Experiments show errors of a few degrees, larger for very small or very oblique stains; analysts average several stains.
What if the width is larger than the length?
Then the axes were swapped – the width is always the shorter axis, so W/L cannot exceed 1.
Why is the real height usually lower?
Drops fly in curved (parabolic) paths, while the tangent method assumes straight lines, so it gives an upper estimate.