Calculate collision distance, initial velocity, coefficient of friction, or gravity from any 3 values with metric and imperial units.
Collision Distance Formula
The calculator uses the stopping distance relationship for an object slowing down due to friction. Enter any 3 values, and the missing value is calculated by rearranging the same formula.
d = v^2 / (2*mu*g)
v = sqrt(2*mu*g*d)
mu = v^2 / (2*g*d)
g = v^2 / (2*mu*d)
- d = collision distance, or stopping distance
- v = initial velocity before slowing begins
- mu = coefficient of friction, unitless
- g = acceleration due to gravity
The collision distance calculation solves for d when you know velocity, friction, and gravity. The initial velocity calculation solves for v when you know the distance needed to stop. The coefficient of friction calculation solves for mu when distance, velocity, and gravity are known. The gravity calculation solves for g, which is useful when checking the same relationship under a different gravitational acceleration.
The calculator converts feet, yards, mph, and ft/s into base metric units before applying the formula, then converts the result back into your selected unit.
Common Reference Values for Collision Distance Calculations
Use these values only as general references. Actual friction depends on surface condition, tire or material condition, temperature, and whether sliding or rolling is involved.
| Surface or contact condition | Typical coefficient of friction | Notes |
|---|---|---|
| Rubber tire on dry asphalt | 0.7 to 0.9 | Common estimate for dry road braking |
| Rubber tire on wet asphalt | 0.4 to 0.6 | Stopping distance increases as friction drops |
| Rubber tire on ice | 0.05 to 0.15 | Very low friction, much longer stopping distance |
| Wood on wood | 0.2 to 0.5 | Varies by finish and surface roughness |
| Steel on steel | 0.1 to 0.2 | Often lower than rubber-road contact |
Speed Conversion Values
| Speed | Meters per second | Feet per second |
|---|---|---|
| 10 mph | 4.4704 m/s | 14.6667 ft/s |
| 30 mph | 13.4112 m/s | 44.0000 ft/s |
| 60 mph | 26.8224 m/s | 88.0000 ft/s |
Example Collision Distance Calculations
Example 1: Find collision distance
You have an initial velocity of 20 m/s, a coefficient of friction of 0.70, and gravity of 9.81 m/s².
d = 20^2 / (2*0.70*9.81)
d = 400 / 13.734 = 29.1255 m
The collision distance is about 29.13 meters.
Example 2: Find initial velocity
You have a collision distance of 50 m, a coefficient of friction of 0.60, and gravity of 9.81 m/s².
v = sqrt(2*0.60*9.81*50)
v = sqrt(588.6) = 24.2611 m/s
The initial velocity is about 24.26 m/s, which is about 54.27 mph.
FAQ
What does collision distance mean in this calculator?
Collision distance means the distance required for an object to stop under frictional deceleration. In a road example, it is the braking or skid distance after slowing begins. It does not include driver reaction time, brake delay, or any distance traveled before braking starts.
Why does speed have such a large effect on collision distance?
The formula uses velocity squared. If speed doubles, the collision distance becomes about 4 times larger, assuming friction and gravity stay the same. This is why a small increase in initial velocity can produce a much longer stopping distance.
What value should you use for gravity?
For most Earth-based calculations, use 9.81 m/s² or 32.174 ft/s². Use a different value only if the calculation is for another planet, moon, or a physics problem that gives a specific gravitational acceleration.