Choose acceleration, kinetic friction coefficient, applied horizontal force, or mass. Enter the other three values for an object already sliding on a level surface, using kg/lb, N/lbf and m/s²/ft/s².

Already sliding on a level surface. Normal force = mg; g = 9.81 m/s².

Positive along the current motion; negative against it.

Coefficient of Friction to Acceleration Formula

The calculator uses Newton’s second law with friction on a level surface. It assumes the object is already sliding, kinetic friction opposes the current motion, and the normal force is mg. Positive force and acceleration follow the current motion; negative acceleration means slowing. It does not determine the threshold for starting from rest.

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 = signed horizontal force, positive along the current sliding direction
  • m = mass of the object
  • g = acceleration due to gravity, 9.81 m/s²
  • mu = nonnegative kinetic friction coefficient, unitless
  • a = signed acceleration along the defined positive axis

Select the desired result in the solve menu and enter the remaining values. Mass must be positive; the friction coefficient must be nonnegative. A zero mass denominator can be nonunique or incompatible, and inputs implying a negative coefficient or nonpositive mass are rejected.

Friction Coefficient Conditions

Actual friction depends on the surface pair, lubrication and test conditions. These entries identify relevant conditions, not recommended coefficients; use a documented kinetic coefficient for your situation.

Surface pair Coefficient input Notes
Wood on wood Use measured μk Varies with grain, finish, and moisture
Rubber on dry concrete Use measured μk High traction surface
Steel on steel, dry Use measured μk Can be much lower if lubricated
Steel on ice Use measured μk Very low friction

Unit Conversions Used

Quantity Conversion to base unit
Mass 1 lb = 0.45359237 kg
Force 1 lbf = 4.4482216152605 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 / s²

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. This describes slowing during the current slide. It must not be used to infer backward motion or motion from rest; static friction and subsequent direction changes require a different force balance.

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.