Friction Force (Static / Kinetic) Calculator
From pushing a box on a floor to whether a block tips and slides on a ramp, the key physics is Coulomb (dry) friction: an object stays at rest as long as the applied force is below μs·N, otherwise it slides and is decelerated by kinetic friction fk = μk·N. Enter mass, incline angle and either custom coefficients or a preset pair (e.g. steel-on-steel, rubber on concrete) to get normal force N, the static and kinetic friction limits, the critical angle of repose θc = arctan(μs), an at-a-glance "will it slide?" verdict and the sliding acceleration a = g·(sin θ − μk·cos θ).
Mass must be > 0; angle must be between 0° and 89°; μs and μk must be ≥ 0.
Normal force N
—
—
Max static friction fs,max
—
—
Kinetic friction fk
—
—
Will the object slide?
—
Formula
N = m·g·cos θ ; fs,max = μs·N ; fk = μk·N ; θc = arctan(μs) ; a = g·(sin θ − μk·cos θ)
Uses Earth standard gravity g = 9.80665 m/s². Tabulated coefficients are typical textbook values (Serway 9e Table 5.1; HyperPhysics) — real values depend on surface finish, temperature and contact pressure.
Formula
N = m·g·cos θ fs,max = μs · N (maximum static friction) fk = μk · N (kinetic friction) θc = arctan(μs) (critical angle / angle of repose) Sliding acceleration a = g·(sin θ − μk·cos θ) when m·g·sin θ > μs·N
- · Friction is independent of contact area (Amontons’ 2nd law) — it depends only on μ and N. It is also roughly independent of sliding speed at low speeds (Coulomb model).
- · Static friction is a "supply-on-demand" force: it automatically matches the applied force up to its limit μs·N, then the surface breaks.
- · Kinetic μk is normally smaller than static μs, which is why a block that just got moving keeps sliding more easily. The tool silently clamps μk to ≤ μs.
- · Critical angle / angle of repose θc = arctan(μs) is the smallest tilt at which the block starts to slide of its own weight — independent of mass.
- · Preset coefficients are typical textbook values from Serway & Jewett 9e Table 5.1 and HyperPhysics; real values depend on surface finish, temperature, contamination and contact pressure.
- · Earth standard gravity g₀ = 9.80665 m/s² (BIPM 1901; NIST SP 811) is used. For other bodies (Moon g ≈ 1.62, Mars g ≈ 3.711) the same formula applies — just plug the new g into μ·m·g·cos θ.
Frequently asked
Why does friction not depend on contact area?
Because the *true* contact area is far smaller than the geometric one. Even polished surfaces are rough at micron scale — only the tiny asperities (peaks) actually touch and carry the load. Increasing the geometric area lowers the pressure per asperity and flattens more of them, so the true contact area stays roughly proportional to the normal force N. Friction therefore scales with μ·N regardless of the apparent area — Amontons’ 2nd law. Exceptions: very flat metals that "cold-weld", or rubber tyres at full contact saturation, can deviate slightly.
Why is the critical angle (angle of repose) independent of mass?
At the moment the block is on the verge of sliding, the down-slope force m·g·sin θ exactly balances the maximum static friction μs·m·g·cos θ. The m·g factor cancels on both sides, leaving sin θ = μs·cos θ → tan θ = μs → θc = arctan(μs). So a bag of rice and a car would (in the pure sliding model) start to slip at the same angle on the same surface. In reality wheels, shape and centre-of-gravity decide whether the object tips before it slides, but for the bare sliding criterion mass really does not enter.
My handbook lists different coefficient values — which should I trust?
Every friction table is a set of *typical* values — 20–50% variation between sources is common because the coefficient depends on surface finish, cleanliness (oil, dust), temperature, contact pressure and whether the surfaces have been "run-in". For engineering design, use measured values from the material/vendor. The presets here are textbook values from Serway & Jewett 9e Table 5.1 and HyperPhysics, suitable for physics homework and rough estimation. Switch to "Custom" if you have measured μs and μk and want an exact result.
Related tools
Ohm's Law Calculator (V / I / R / P)
Enter any two of voltage, current, resistance, or power — the calculator solves for the other two using V = IR and P = VI.
Speed, Distance & Time Calculator
Enter any two of distance, time and speed to get the third — with km/h, mph, m/s, km, miles, hours and minutes supported.
Density Calculator (mass / volume)
Compute density from mass and volume (ρ = m / V), or solve for the missing variable. Built-in reference table for 19 common substances.
Projectile Motion Calculator
Enter launch speed, angle and height to compute projectile range, peak height and flight time (no air resistance). Pick from Earth, Moon, Mars and more.
Wind Chill Calculator
Compute the wind chill (feels-like temperature) from air temperature and wind speed using the 2001 Environment Canada / US NWS formula, with frostbite risk levels.
Dew Point Calculator
Compute dew point from air temperature and relative humidity using the Magnus formula — handy for HVAC, photography and weather analysis.
Kinetic Energy Calculator (KE = ½ m v²)
Compute kinetic energy KE = ½ m v² with mixed units (kg / g / lb and m/s / km/h / mph) and see the result in joules, kilojoules, food calories, foot-pounds and watt-hours.
Half-Life & Exponential Decay Calculator
Enter any three of initial amount, remaining amount, elapsed time and half-life to solve for the fourth — useful for radioactive decay, drug pharmacokinetics and radiometric dating.
Resistor Color Code Calculator (4 / 5 band)
Pick the colour bands and instantly read the resistance and tolerance — 4-band and 5-band notations supported, with Ω / kΩ / MΩ formatting and a closest E12 / E24 preferred-value check.
GPS Distance Calculator (Haversine)
Enter two latitude/longitude pairs to compute the great-circle distance using the haversine formula (km, miles, nautical miles), with bearing and midpoint.
Solution Dilution Calculator (C₁V₁ = C₂V₂)
Solve any one of C₁, V₁, C₂, V₂ from the dilution equation C₁V₁ = C₂V₂ — a daily lab essential for chemistry, biology and pharmacy work.
Decibel (dB) Sum Calculator
Two 80 dB sound sources do not equal 160 dB. Enter multiple dB values to compute the combined SPL, and subtract background noise to recover the signal alone.
Resistor Parallel / Series Calculator
Enter up to 8 resistor values to see the series total (R₁ + R₂ + …) and the parallel total (1 / Σ(1/Rᵢ)) at the same time.
Wavelength ↔ Frequency Calculator
Convert between electromagnetic wavelength and frequency via c = λf, with the matching spectrum band (radio / microwave / visible / X-ray / γ) and photon energy.
Tank Volume Calculator
Compute the capacity of vertical or horizontal cylindrical, rectangular and spherical tanks, including partial-fill volumes at a given liquid level.
Pendulum Period Calculator (T = 2π√L/g)
Enter the pendulum length and local gravity to get the period, frequency and angular frequency, with Earth/Moon/Mars/Jupiter presets — and reverse-solve for the length needed to hit a target period.
Heat Index Calculator
Enter air temperature and relative humidity to get the apparent temperature (NOAA Rothfusz heat index) and the corresponding heat-stress risk band.
Vehicle Stopping Distance Calculator
Enter speed, reaction time and road friction to estimate reaction, braking and total stopping distance.
Snell's Law Refraction Calculator
Enter the refractive indices of two media and an angle of incidence — get the refraction angle and critical angle from Snell's law (n₁ sin θ₁ = n₂ sin θ₂).
Capacitor Energy Calculator
Enter capacitance (F, mF, µF, nF, pF) and voltage to compute the stored energy (E = ½CV²) and charge (Q = CV) on a capacitor.
Boiling Point at Altitude Calculator
Enter altitude to compute the boiling point of water (°C / °F) and local air pressure using the ICAO standard atmosphere and the Antoine equation — useful for hiking, cooking and high-altitude baking.
Specific Heat (Q = mcΔT) Calculator
Solve Q = m × c × ΔT for any one of heat energy, mass, specific heat capacity or temperature change — with presets for water, aluminium, iron, copper, glass, air and more.
pH and Hydrogen Ion Concentration Calculator
Convert between pH, pOH, hydrogen-ion concentration [H⁺] and hydroxide concentration [OH⁻] — with acid / neutral / alkaline classification.
Ideal Gas Law (PV = nRT) Calculator
Pick the unknown (P, V, n or T), enter the other three and PV = nRT is solved instantly — works in Pa / kPa / atm / bar / mmHg / psi, m³ / L / mL, mol / mmol / kmol and K / °C / °F.
Coulomb's Law Calculator
Enter two point charges and the separation distance to compute the electrostatic force between them via F = kₑ·q₁·q₂/r² (attractive or repulsive).
Newton's Law of Universal Gravitation Calculator
Enter two masses and the distance between them to compute the gravitational attraction via F = G·m₁·m₂/r².
Thin Lens Equation Calculator
Given any two of the three quantities (object distance u, image distance v, focal length f), solve for the remaining one and the lateral magnification.
Distance to Horizon Calculator
Enter the observer eye height above the surface to compute the distance to the geometric and refraction-corrected horizon.
Hooke's Law (Spring Force) Calculator
Given any two of spring constant k, displacement x or restoring force F, solve for the third and the elastic potential energy U = ½kx².
Buoyancy Force (Archimedes' Principle) Calculator
Enter fluid density, submerged volume and gravitational acceleration to compute the buoyant force F = ρ V g, plus whether the object floats, sinks or stays neutral.
Voltage Divider Calculator
Enter the input voltage and two series resistor values to find the divider output voltage, current and power dissipated in each resistor.
Escape Velocity Calculator
Enter the mass and radius of a celestial body (or pick Earth, Moon, Mars and other presets) to compute the minimum surface launch speed v = √(2GM/r) needed to escape its gravity.
Doppler Shift Frequency Calculator
Enter the source frequency, observer/source velocities and wave speed (sound or light) to compute the observed frequency shift due to the Doppler effect.
Newton's Law of Cooling Calculator
Enter initial temperature, ambient temperature, cooling constant and elapsed time to estimate an object's temperature with T(t) = T∞ + (T₀ − T∞)·e^(−kt), plus half-cooling time and time constant.
Centripetal Force Calculator
Enter mass and radius, then linear speed, angular speed or period, and instantly read off centripetal force F = m·v²/r, centripetal acceleration, tangential speed, angular speed, period and frequency.
LC Resonant Frequency Calculator
Enter inductance L (H) and capacitance C (F) to compute the resonant frequency f = 1 / (2π√(LC)) of an LC tank circuit, plus its period and angular frequency.
Speed of Sound in Air Calculator
Enter the air temperature and compute the speed of sound in dry air using v = 331.3 × √(1 + T/273.15) — output in m/s, km/h, mph, ft/s plus the "count-the-seconds" thunder distance rule.
Reynolds Number Calculator
Enter fluid density, velocity, characteristic length and viscosity to compute the Reynolds number and classify the flow as laminar, transitional or turbulent.
Spring Potential Energy Calculator
Enter the spring constant k and displacement x to instantly compute the elastic potential energy stored in a Hookean spring via U = ½·k·x², with conversions to kJ, kcal, ft·lbf and Wh for easy comparison.
Beer-Lambert Law Absorbance Calculator
Use A = ε·c·ℓ to compute absorbance, transmittance and concentration — any three of the four inputs determines the fourth.
Kepler's Third Law (Orbital Period) Calculator
Compute orbital period from semi-major axis and central body mass via T² = 4π²·a³/GM, or invert to recover the semi-major axis — with presets for the Sun, Earth, Moon and Jupiter.
Drag Force Calculator
Enter fluid density, velocity, drag coefficient Cd and frontal area and compute the drag force from Fd = ½·ρ·v²·Cd·A — handy for cycling, automotive, ballistic and skydiving scenarios.
Hydrostatic Pressure Calculator
Compute the hydrostatic pressure P = ρ·g·h from fluid density, depth and gravity, and convert it to kPa, bar, psi, atm, mmHg and metres of water — useful for diving, aquariums and piping.
Buffer pH (Henderson–Hasselbalch) Calculator
Enter pKa together with the conjugate-base [A⁻] and weak-acid [HA] concentrations and apply the Henderson–Hasselbalch equation to compute buffer pH, the buffer ratio and the effective buffering range.
Gear Ratio Calculator
Enter driving and driven gear tooth counts plus input RPM and torque to compute gear ratio, output RPM, output torque and mechanical advantage.
Molarity Calculator
Enter solute mass, molecular weight and solution volume to compute molarity (mol/L); solve for any one unknown.
Earthquake Magnitude ↔ Energy Calculator
Convert moment magnitude (Mw) to released energy (joules and TNT equivalent) via the Gutenberg–Richter relation log₁₀E = 1.5M + 4.8, with a comparison to landmark historical earthquakes.
Percent Yield Calculator (Chemistry)
Enter the actual mass of product recovered and the theoretical yield to compute % yield = actual ÷ theoretical × 100%, with an indicative classification (poor / moderate / good / excellent).
Moment of Inertia Calculator (Common Shapes)
Pick a common shape (solid sphere, hollow sphere, solid cylinder, thin-walled cylinder, thin disk, slender rod about centre or end, rectangular plate) and enter mass and dimensions to get the rotational moment of inertia I = k·m·r² / k·m·L².
Air Density Calculator (Temperature, Pressure, Humidity)
Enter air temperature, barometric pressure and relative humidity to compute air density (kg/m³) via the CIPM partial-pressure form and the Magnus-Tetens saturation vapour pressure — useful for cyclists, runners, pilots and aerodynamics estimates.
Free Fall Calculator (Time, Velocity, Kinetic Energy)
Enter a fall height (and optional mass / gravity) to compute fall time, impact velocity and kinetic energy via h = ½·g·t² and v = √(2·g·h). Preset gravities for Earth, Moon, Mars and more.
Molar Mass Calculator (Chemical Formula)
Enter a chemical formula (e.g. H2SO4, Ca(OH)2, CuSO4·5H2O) and the tool sums the IUPAC standard atomic weights element by element to return the molar mass in g/mol — useful for chemistry homework and lab weighing.
Newton's Second Law Calculator (F = m·a)
Enter any two of force, mass and acceleration and the tool solves for the third — handy for high-school physics, machine design, vehicle braking and elevator safety factors.
Mass ↔ Moles Converter (n = m / M)
Enter mass and molar mass (g/mol), or moles, and the tool converts via n = m / M, also reporting the particle count N = n · Nₐ — the everyday workhorse of chemistry lab weighing and stoichiometry problems.
Lorentz Factor Calculator (Time Dilation γ)
Enter a velocity v (as a fraction of c or in m/s) and compute the special-relativity Lorentz factor γ = 1/√(1 − v²/c²), together with the time-dilation factor, the length-contraction ratio and the relativistic kinetic energy.