About the Angle of Impact Calculator
This calculator applies the standard bloodstain pattern analysis (BPA) formula used by crime scene investigators and forensic students to determine the angle at which a blood drop struck a surface. A round drop that hits a surface head-on, at 90°, leaves a circular stain. At any shallower angle, the drop elongates into an ellipse as it strikes and drags, and the ratio between that ellipse's width and length is a direct, trigonometric measure of the impact angle.
The formula
For a bloodstain with a measured length (the long axis, in the direction of travel) and width (the short axis, perpendicular to it), the angle of impact is:
θ = arcsin(width ÷ length)
Because width can never exceed length for a real stain, the ratio width/length stays between 0 and 1, giving an angle between 0° (a razor-thin stain from a near-parallel strike) and 90° (a circular stain from a perpendicular strike).
Estimating origin height with the tangent method
Once the angle of impact is known and the horizontal distance from the stain to the point where several stains' flight paths converge has been measured — typically by physically stringing lines back from a group of stains to where they meet, or with a laser trajectory rod — the height of the blood source above that convergence point follows from simple right-triangle trigonometry:
height = distance × tan(θ)
This is the classic "stringing" or tangent method taught in bloodstain pattern analysis: the angle of impact sets the slope of the drop's flight path, and the horizontal run to the convergence point multiplied by that slope gives the rise, i.e., how high above the surface the blood originated.
How to get the best results
- Measure length and width from a clear, undistorted, roughly elliptical stain — one that hasn't merged with a neighboring stain or picked up satellite spatter along its edges.
- Keep length and width in the same unit (millimeters); the ratio is unitless so the formula works regardless of scale, but mixing units will throw off the angle.
- For the origin-height estimate, use the horizontal distance measured along the target surface to the point of convergence, not a straight-line (slant) distance to the stain.
Practical context
This tool automates the trigonometry; it does not replace scene documentation, calibrated photography, or trained judgment. Real bloodstain pattern casework should follow validated laboratory protocols, and any conclusions used in an investigation or courtroom should be produced or reviewed by a qualified forensic analyst.