Friction Calculator
Calculate friction force, normal force and the force needed to move an object.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
About this calculator
Simplified incline model: the applied force and gravity component act downhill. Static friction balances that force up to coefficient × normal force; once motion starts, the same coefficient is used as a friction estimate. Real surfaces may have different static and kinetic coefficients.
Worked example
calculated with the default values below
Mass of the object 10 kg · Coefficient of friction 0.4 · Surface angle 0 degrees · Applied force down the slope 100 N · Gravity 9.81 m/s² Weight 98.10 N · Normal force 98.10 N · Friction force in this model 39.24 N · Additional downhill force to start motion 39.24 N · Net force 60.76 N · Acceleration 6.08 m/s² · Will it move Yes — it accelerates
Method and assumptions
Friction capacity is coefficient × normal force; the incline resolves weight into normal and downhill components. The page uses one coefficient for both the breakaway threshold and moving friction, unlike separate static and kinetic coefficients in the reference. Its applied force is added in the downhill direction; it is a simplified one-dimensional model.
Data sources
Disclaimer
These calculators give general conversion results. Rounding and the precision of the value you enter both affect the output, so treat displayed decimals as indicative rather than exact.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
N = mg cos θ; G = mg sin θ; Fmax = μN; D = appliedForce + G; if D ≤ Fmax: friction = D, net = a = 0; otherwise friction = Fmax, net = D − Fmax, a = net ÷ m
- m
- mass
- g
- gravitational acceleration
- θ
- incline angle in degrees
- μ
- friction coefficient
- a
- acceleration
- P
- applied force downhill
N = mg cos θ; downhill gravity = mg sin θ; maximum static friction = μN. Downhill drive is applied force + gravity component. Below μN, static friction balances the drive and net force/acceleration are zero; above it, the same μ estimates moving friction.
Frequently asked questions
Why does a slope reduce the friction that holds an object?
On a slope, the normal force is weight × cosine(angle), while gravity contributes weight × sine(angle) downhill. Static friction balances the downhill force up to coefficient × normal force. This simplified model treats the entered force as downhill and reuses one coefficient after motion starts; real surfaces may have different static and kinetic friction.
Which inputs and limits apply to Friction Calculator?
Use the units shown beside each field. These are form limits, not recommended settings. Mass of the object: 0–1,000,000 kg; Coefficient of friction: 0–5; Surface angle: 0–89 degrees; Applied force down the slope: 0–10,000,000 N; Gravity: 0.1–100 m/s² Friction capacity is coefficient × normal force; the incline resolves weight into normal and downhill components. The page uses one coefficient for both the breakaway threshold and moving friction, unlike separate static and kinetic coefficients in the reference. Its applied force is added in the downhill direction; it is a simplified one-dimensional model.
What is a complete worked example for Mass of the object = 10 kg; Coefficient of friction = 0.4?
Inputs: Mass of the object = 10 kg; Coefficient of friction = 0.4; Surface angle = 0 degrees; Applied force down the slope = 100 N; Gravity = 9.81 m/s². Calculation: N = mg cos θ; G = mg sin θ; Fmax = μN; D = appliedForce + G; if D ≤ Fmax: friction = D, net = a = 0; otherwise friction = Fmax, net = D − Fmax, a = net ÷ m. Results: Weight = 98.10 N; Normal force = 98.10 N; Friction force in this model = 39.24 N; Additional downhill force to start motion = 39.24 N; Net force = 60.76 N; Acceleration = 6.08 m/s²; Will it move = Yes — it accelerates.