Calculate the force needed to move an object or load over a flat surface or up a ramp, using typical friction for common surfaces or your own coefficient.
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Moving Force Formula
The calculator uses one of three formulas depending on the scenario you select.
Level surface, steady speed:
Up a ramp, steady speed:
Level surface with acceleration:
- F = force needed to move the load (N or lbf)
- W = weight of the load (N or lbf), where W = m * g
- m = mass in kilograms in the SI formulas; convert pounds or grams first
- μ = coefficient of friction between the load and the surface
- θ = ramp angle from horizontal
- a = desired acceleration (m/s² or ft/s²)
- g = selected gravity (m/s²); standard Earth defaults to 9.80665, Moon estimate 1.62, Mars estimate 3.71, or a custom positive value
Assumptions: a rigid surface and applied force parallel to it, with forward sliding on level ground or uphill on a ramp. Use the kinetic coefficient for sliding. The static basis represents the limiting force at impending forward or uphill motion, with zero acceleration; actual static friction may be below μsN. This model ignores rolling, air drag, tipping and deformation and is not a safe-handling or equipment rating.
Reference Values
Approximate illustrative coefficients from OpenStax Table 6.1 are shown below where available. Actual surface conditions matter; the cardboard/carpet pair has no value supplied by that table. Measure or obtain appropriate coefficients for the actual materials.
| Material pair | Static μ | Kinetic μ |
|---|---|---|
| Wood on wood | 0.50 | 0.30 |
| Steel on steel (dry) | 0.60 | 0.30 |
| Steel on steel (oiled) | 0.05 | 0.03 |
| Rubber on dry concrete | 1.00 | 0.70 |
| Rubber on wet concrete | 0.5–0.7 | 0.3–0.5 |
| Cardboard on carpet | Measure | Measure |
| PTFE (Teflon) on steel | 0.04 | 0.04 |
Required force divided by load weight is a dimensionless resistance ratio. It does not determine how many people can move a load or whether a task is safe:
| Force / weight ratio | Ratio interpretation |
|---|---|
| Below 0.10 | Force below 10% of load weight |
| 0.10 to 0.35 | Force 10% to 35% of load weight |
| 0.35 to 0.70 | Force 35% to 70% of load weight |
| Above 0.70 | Force above 70% of load weight; no handling rating implied |
Worked Example
You want to push a 100 kg crate across a wood floor (μ = 0.30) and accelerate it at 1 m/s².
- Weight: W = 100 × 9.80665 = 980.7 N
- Friction: μW = 0.30 × 980.7 = 294.2 N
- Acceleration force: ma = 100 × 1 = 100 N
- Total: F = 100 + 294.2 = 394.2 N (about 89 lbf)
FAQ
Static or kinetic friction? Use kinetic μ for sliding. Use static μ only for the impending-motion threshold at zero acceleration; equality is the limiting balance and actual static friction can be smaller. Static coefficients are often greater than kinetic values, but not always.
Why is the ramp force higher even at the same μ? On a ramp you fight gravity directly through the sin θ term in addition to friction. At 10° with μ = 0.30, the force is roughly 47% of the load weight versus 30% on a level floor.
Does this work for wheeled loads? This calculator models sliding rather than rolling. Do not treat a sliding-friction coefficient as a universal rolling-resistance value; wheels, bearings, tire deformation, surface and other losses require an appropriate separate model.
