How this calculator works
Bloodstain pattern analysis treats a falling drop as a small sphere. When it hits a surface at a shallow angle, the drop spreads farther along the direction of travel than across it, so the stain becomes oval. The width of the stain is the same as the drop diameter seen head on, while the length is stretched by the reciprocal of the sine of the angle. The angle is therefore the inverse sine of width divided by length. The relationship assumes a smooth, non-absorbent surface and a single drop; rough fabric, a steep surface or a drop that splashes can all break the assumption.
Formula
angle of impact = arcsin(width / length). stain width = length x sin(angle). stain length = width / sin(angle). The elongation is length divided by width, which equals 1 / sin(angle).
Worked example
A stain 12 mm long and 6 mm wide has an angle of impact of arcsin(6 / 12) = 30 degrees. A stain at 45 degrees with a 10 mm length is 10 x sin 45 = 7.07 mm wide. A 5 mm wide stain from a 30 degree impact would have been 5 / sin 30 = 10 mm long.
Advertisement
Frequently asked questions
Why is the angle always between 0 and 90 degrees?
The width of a stain cannot exceed its length, because the drop can only stretch along its path. A ratio of one is a perpendicular impact at 90 degrees, and a very small ratio approaches a grazing impact at 0 degrees.
Can I use this on fabric?
Only with caution. Fabric wicks blood outward and can make the stain rounder or more irregular, which biases the angle. Investigators often use a test stain on the same material to calibrate the estimate.
What does a negative or impossible result mean?
If the measured width is greater than the length, the numbers are inconsistent or the stain is not a single drop. The calculator refuses that input rather than returning a meaningless angle.
Is the angle measured from the surface or from the vertical?
It is measured from the surface, so a drop falling straight down is 90 degrees and a drop travelling almost parallel to the surface is close to 0 degrees. Some reports use the complement, so check which convention a report uses.