Calculate static friction (fs = μs·FN), kinetic friction (fk = μk·FN), coefficient of friction (μ), normal force on flat and inclined surfaces, and angle of repose with the free Friction Calculator.
88.2 lbf (39.99 kgf) • Normal Force: 490.35 N • Max Static Friction: 490.35 N
Threshold to slip
Perpendicular load
Critical slip angle
\(W_f = -f_k \cdot d\)
Dissipated heat
40.0 kgf
In classical mechanics and tribology, friction is the contact resistive force that opposes the relative tangential sliding or rolling motion between two solid surfaces in contact. Microscopic contact surfaces are never completely smooth; they feature microscopic peaks and valleys called asperities that mechanically interlock and form instantaneous cold welds under normal force.
The self-adjusting holding force that prevents stationary objects from slipping until the applied shear force exceeds \(f_{s,\text{max}} = \mu_s F_N\).
The continuous sliding resistance encountered once motion begins: \(f_k = \mu_k F_N\). In almost all physical systems, \(\mu_k < \mu_s\).
The minute resistance generated by deformation of rolling cylinders or spheres, typically 10 to 100 times smaller than sliding friction.
| Friction Quantity | Formula | Description |
|---|---|---|
| Maximum Static Friction (\(f_{s,\text{max}}\)) | $$f_{s,\text{max}} = \mu_s F_N$$ | Peak breakaway threshold in Newtons (N) |
| Kinetic Sliding Friction (\(f_k\)) | $$f_k = \mu_k F_N$$ | Steady-state sliding drag force in Newtons (N) |
| Normal Force on Flat Surface | $$F_N = m g$$ | Perpendicular gravitational reaction load |
| Normal Force on Incline (\(\theta\)) | $$F_N = m g \cos\theta$$ | Perpendicular component on ramp |
| Angle of Repose (\(\theta_c\)) | $$\theta_c = \arctan(\mu_s)$$ | Maximum ramp tilt before slip occurs |
| Friction Work Dissipation (\(W_f\)) | $$W_f = -f_k d \implies Q = f_k d$$ | Thermal energy dissipated in Joules (J) |
Choose between Horizontal Flat Surface, Inclined Ramp, or Direct Normal Force input.
Input object mass in kilograms, grams, or pounds, and enter the slope angle if working with an incline.
Select material pairings (e.g., Rubber on Concrete, Steel on Steel, Teflon on Steel) or input custom \(\mu_s\) and \(\mu_k\).
Inspect breakaway static threshold, sliding resistance, angle of repose, and step-by-step mathematical proofs.
Why ABS maximizes braking force by preventing wheel lockup:
When tires roll during threshold braking, the contact patch experiences static friction (\(\mu_s \approx 1.0\) on dry asphalt). If the driver slams the brakes and locks the wheels, the tire transitions into kinetic sliding friction (\(\mu_k \approx 0.8\)), reducing braking force by \(20\%\) and lengthening stopping distance by over \(25\%\). Anti-Lock Braking Systems (ABS) modulate brake line hydraulic pressure 15 to 20 times per second to keep tire slip in the peak static friction envelope.
Calculates exact angles of repose and holding normal forces to prevent cargo palettes, vehicles, and construction materials from sliding down ramps.
Enables mechanical engineers to size linear actuators and drive motors by determining the exact breakaway static threshold force (\(f_{s,\text{max}}\)).
Computes mechanical work converted to thermal energy (\(Q = f_k d\)), preventing brake rotor overheating and thermal fade.
Seamlessly switches between flat surfaces (\(F_N = mg\)), inclined ramps (\(F_N = mg\cos\theta\)), and direct normal force inputs.
Evaluates both peak static breakaway resistance and steady-state dynamic sliding forces in parallel.
Pre-loaded with static and kinetic coefficients for rubber, steel, wood, PTFE/Teflon, and ice interfaces.
How friction powers pulleys, winches, and conveyor systems:
When flexible belts, ropes, or cables wrap around a cylindrical capstan through total wrap angle \(\theta\) (in radians), friction amplifies holding force exponentially according to the Euler-Eytelwein Capstan Equation:
With a friction coefficient of \(\mu = 0.3\) and 3 full turns around a bollard (\(\theta = 6\pi \approx 18.85\text{ rad}\)), the amplification factor is \(e^{0.3 \times 18.85} \approx 285\). A sailor holding just \(10\text{ lbs}\) of rope tension can effortlessly restrain a \(2,850\text{-lb}\) mooring load.
Comprehensive answers to common questions about friction formulas, normal forces, static vs. kinetic coefficients, and angles of repose.
