Estimate Speed or Distance of Objects with the Hand
Calculator for speed and distance of moving objects, like planes or cars. Stretch one arm and take the time it needs, until the object has passed behind the hand, which means that it has passed a certain angle. The stretched pinky (fingertip for each finger) covers about 1 degree, the thumb 2 degrees, the three middle fingers together about 5 degrees, a fist about 10 degrees and a fist with stretched pinky and thumb about 20 degrees. If distance or speed are known, the other value can be calculated. This assumed that the object moves perpendicular to the line of sight, i.e., that the direction of movement is 90 degrees.
Formula: r = v * t / α * sin(β)
If the direction of movement is not perpendicular to the viewing direction, the value must be multiplied by the sine of the direction angle. However, the angle of movement is very difficult to estimate. As an average value, 45 degrees can be assumed. Then the sine is 0.71, and accordingly, the time or distance decreases, or the speed increases, by about 40 percent. This simplification is, of course, subject to considerable uncertainty.
Example: An airplane takes one second to disappear behind a thumb and reappear. It moves perpendicular to the direction of view. The angle is therefore two degrees for the width of the thumb. If the airplane is a passenger plane that is not currently taking off or landing, then a cruising speed of approximately 900 kilometers per hour can be assumed. This results in a calculated distance of just over 7 kilometers for the airplane. The biggest uncertainty here is estimating the time interval. Estimating one second is difficult. The calculated distance changes linearly with the measured time. For a duration of half a second, the distance is also halved.
Last updated on 01/19/2026. Author: Jürgen Kummer
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