Calculate the missing mass, force, coefficient of friction, or acceleration from any 3 inputs, with kg or lb, N or lbf, and m/s² or ft/s².
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Coefficient of Friction to Acceleration Formula
The calculator uses Newton’s second law with friction on a level surface. The applied moving force must overcome friction first, and any remaining force accelerates the object.
F = m*g*mu + m*a
Rearranged forms used by the calculator:
a = (F - m*g*mu) / m
mu = (F - m*a) / (m*g)
m = F / (g*mu + a)
- F = moving force applied to the object
- m = mass of the object
- g = acceleration due to gravity, 9.81 m/s²
- mu = coefficient of friction, unitless
- a = acceleration of the object
If you leave acceleration blank, the calculator uses the applied force, mass, and coefficient of friction to find the resulting acceleration. If you leave coefficient of friction blank, it solves for the coefficient needed to match the given force and acceleration. If you leave force blank, it finds the moving force required to overcome friction and produce the entered acceleration. If you leave mass blank, it finds the mass that fits the entered force, friction coefficient, and acceleration.
Common Friction Coefficient Ranges
Actual friction depends on surface condition, material, lubrication, and whether the object is starting from rest or already sliding.
| Surface pair | Typical coefficient range | Notes |
|---|---|---|
| Wood on wood | 0.25 to 0.50 | Varies with grain, finish, and moisture |
| Rubber on dry concrete | 0.60 to 1.00 | High traction surface |
| Steel on steel, dry | 0.40 to 0.80 | Can be much lower if lubricated |
| Steel on ice | 0.01 to 0.05 | Very low friction |
Unit Conversions Used
| Quantity | Conversion to base unit |
|---|---|
| Mass | 1 lb = 0.453592 kg |
| Force | 1 lbf = 4.44822 N |
| Acceleration | 1 ft/s² = 0.3048 m/s² |
Example Problems
Example 1: Find acceleration
An object has a mass of 20 kg. The coefficient of friction is 0.30, and the moving force is 100 N.
a = (F - m*g*mu) / m
a = (100 - 20*9.81*0.30) / 20
a = 2.057 m/s^2
The acceleration is about 2.057 m/s².
Example 2: Find required moving force
An object has a mass of 50 kg, a coefficient of friction of 0.20, and a desired acceleration of 1.5 m/s².
F = m*g*mu + m*a
F = 50*9.81*0.20 + 50*1.5
F = 173.1 N
The required moving force is 173.1 N.
FAQ
Can acceleration be negative?
Yes. A negative acceleration means the friction force is larger than the applied moving force in the direction of motion. In the formula, this happens when F is less than m*g*mu. Physically, the object would slow down if it was already moving, or it may not start moving if the coefficient represents static friction.
Is the coefficient of friction unitless?
Yes. The coefficient of friction is a ratio of friction force to normal force, so it has no units. You should enter it as a decimal, such as 0.25, 0.40, or 0.75.
Does this work for ramps or angled forces?
No. This calculation assumes a level surface and a horizontal moving force. For an incline or an angled pull, the normal force changes, so the friction term is not simply m*g*mu.
