About

Bloodstain pattern analysis (BPA) reconstructs events at a crime scene by examining the geometry of blood drops on surfaces. A blood drop striking a surface at an angle produces an elliptical stain. The angle of impact θ is determined by the ratio of the stain's w (minor axis, width) to its l (major axis, length) using arcsin(w ÷ l). A perpendicular drop (θ = 90°) produces a circle. Shallower angles elongate the ellipse. Measurement error of even 0.5mm can shift the computed angle by several degrees, so precision matters. This calculator assumes an idealized elliptical stain on a non-porous, flat surface. Real substrates (fabric, rough concrete) distort stain geometry and introduce systematic error. Results should be cross-validated with stringing or virtual convergence methods per SWGSTAIN guidelines.

Formulas

The angle of impact is derived from the trigonometric relationship between the minor and major axes of an elliptical bloodstain.

θ = arcsin(wl)

Where θ = angle of impact (measured from the surface plane), w = width of the bloodstain (minor axis of the ellipse, perpendicular to the direction of travel), and l = length of the bloodstain (major axis of the ellipse, along the direction of travel). The ratio w ÷ l must satisfy 0 < w ÷ l ≤ 1. Conversion to radians uses:

θ_rad = θ_deg × π180

The sine of the impact angle equals the eccentricity ratio: sin(θ) = w ÷ l. At θ = 90°, the stain is circular (w = l). As θ decreases toward 0°, the stain elongates and w ÷ l approaches 0.

Reference Data

Width/Length Ratio	Impact Angle (°)	Stain Shape	Typical Scenario
0.05	2.87°	Extremely elongated	Very shallow cast-off on wall
0.10	5.74°	Highly elongated	Low-angle cast-off
0.15	8.63°	Very elongated	Shallow impact spatter
0.20	11.54°	Elongated	Low trajectory spatter
0.30	17.46°	Moderately elongated	Angled impact spatter
0.40	23.58°	Oval	Mid-angle spatter
0.50	30.00°	Wide oval	Common impact angle
0.60	36.87°	Broad oval	Moderate-angle impact
0.70	44.43°	Near-circular oval	Steep-angle impact
0.75	48.59°	Slightly oval	High-angle spatter
0.80	53.13°	Nearly circular	Near-vertical trajectory
0.85	58.21°	Nearly circular	Steep drip pattern
0.90	64.16°	Slightly oval	Near-perpendicular drip
0.95	71.81°	Near-circle	Almost vertical impact
1.00	90.00°	Perfect circle	Perpendicular (90°) drop

Frequently Asked Questions

By definition, the width (w) is the minor axis and the length (l) is the major axis of the elliptical stain. The ratio w ÷ l must be between 0 and 1 inclusive. If your measured width exceeds the length, the axes have been confused - rotate your measurement 90°.

Rough or porous surfaces (concrete, fabric, untreated wood) cause blood to spread irregularly, producing spines, scalloping, or satellite spatters that distort the true ellipse boundary. This makes accurate measurement of w and l difficult and introduces systematic error. SWGSTAIN recommends measuring to the "parent stain" edge, excluding spines. On very rough surfaces, the calculated θ may deviate by 5° to 15° from the true angle.

A measurement error of 0.5mm in width on a 3mm wide stain changes the ratio by roughly 17%, which can shift the result by 3° to 8° depending on the angle range. Use calipers or calibrated photographic analysis software. Digital measurement from scaled photographs is standard practice in modern BPA.

No. This tool calculates the angle of impact for a single stain. Determining the area of origin requires multiple stains. The 2D point of convergence is found by extending the major axes of several stains on a surface until they intersect. The 3D area of origin then uses each stain's θ with trigonometric projection (tangent method) or stringing. This tool provides the θ values needed as inputs for that reconstruction.

No. The arcsin(w ÷ l) formula assumes a perfect sphere impacting a flat plane. In reality, blood drops oscillate between oblate and prolate shapes during flight due to air resistance and initial deformation. For drops traveling short distances (< 1m), this effect is minimal. For longer flight paths, the oscillation can alter stain morphology and introduce error of 2° to 5°.

Below approximately 5° to 10°, stains become so elongated that the leading edge is difficult to define. Tail and spine artifacts dominate the stain shape. The parent stain boundary becomes ambiguous, making accurate measurement of l unreliable. Results below 10° should be reported with a higher uncertainty margin.