Mendeleev · Physics

Physics tools

Choose the quantity to find, enter what you know, and see the formula, units and reasoning immediately. Notation is adapted to English-language physics conventions.

59 tools · mechanics · fluids · electricity · waves · thermal · modern physics · space

Mechanics

Motion, forces, oscillations and energy

KE = ½mv²Kinetic energy calculatorCalculate kinetic energy from mass and speed, or solve for mass or speed. Unit conversions are handled automatically.PE = mghGravitational potential energyCalculate gravitational potential energy near Earth from mass, gravity and height.v = d / tSpeed, distance and timeCalculate speed, distance or travel time from the other two quantities, with common unit conversions.a = (v₂ − v₁) / ΔtAcceleration calculatorCalculate average acceleration from initial speed, final speed and elapsed time, or solve for any one of those quantities.F_net = maNewton’s second law: force, mass, accelerationUse F = ma to calculate net force, mass or acceleration in a one-dimensional situation.W = mgWeight calculatorCalculate weight from mass and gravitational field strength, or solve for mass or g.p = mvMomentum calculatorCalculate linear momentum from mass and velocity, or solve for mass or velocity.W = Fd cos θWork done by a forceCalculate work from force, displacement and the angle between them.P = W / ΔtMechanical powerCalculate average power from work or transferred energy and elapsed time.F = kxHooke’s law calculatorCalculate force, spring constant or extension in the linear elastic regime.E = ½kx²Elastic potential energyA deformed spring stores elastic potential energy. Because extension is squared, doubling the deformation multiplies the stored energy by four.T = 2π√(L/g)Simple pendulum periodThe period of a simple pendulum depends on its length and on gravity, not on the bob’s mass.T = 2π√(m/k)Mass–spring oscillator periodFor an ideal mass–spring oscillator, the period increases with mass and decreases as the spring becomes stiffer.a₍c₎ = v²/rCentripetal accelerationEven at constant speed, circular motion involves acceleration because the velocity direction continually changes.F₍c₎ = mv²/rCentripetal forceCentripetal force is the inward resultant force required to keep an object moving along a circular path.ω = 2πfAngular speed and frequencyAngular speed describes how quickly an angle changes. One full revolution corresponds to 2π radians.v = ωrTangential speedTangential speed links rotational motion to linear motion at a given distance from the rotation axis.J = FΔtImpulse, force and timeImpulse measures the effect of a force acting over a time interval and equals the change in momentum.η = Eᵤ/EᵢₙEnergy efficiencyEfficiency compares useful energy obtained with the energy supplied to a system.

Fluids

Pressure, buoyancy and flow

P = F / APressure, force and areaCalculate pressure, force or contact area from P = F/A.ρ = m / VDensity, mass and volumeCalculate density, mass or volume with automatic conversion between common SI and laboratory units.Δp = ρghHydrostatic pressureIn a fluid at rest, pressure increases with depth because of the weight of the fluid above.Fᵦ = ρgVBuoyant forceAn immersed object experiences an upward force equal to the weight of the displaced fluid.Q = V/ΔtVolume flow rateVolume flow rate tells you how much fluid passes through a section per unit time.A₁v₁ = A₂v₂Continuity equationFor steady incompressible flow, the same volume flow rate passes through every cross-section of a pipe.F₁/A₁ = F₂/A₂Hydraulic pressIn an ideal hydraulic system, the same pressure is transmitted through the fluid, allowing force to be multiplied by using a larger piston area.

Electricity

Charges, capacitors and circuits

V = IROhm’s law calculatorCalculate voltage, current or resistance for an ohmic component.P = VIElectric power calculatorCalculate electric power, voltage or current in a DC or purely resistive situation.E = PΔtElectric energy, power and timeCalculate electrical energy, average power or operating time, with joules and watt-hours.Q = IΔtElectric charge, current and timeCalculate transferred electric charge from current and time, or solve for current or duration.R_series = ΣR · 1/R_parallel = Σ(1/R)Resistors in series or parallelCalculate equivalent resistance for several resistors connected in series or in parallel.F = k|q₁q₂|/r²Coulomb’s lawTwo point charges exert an electrostatic force whose magnitude is proportional to both charges and decreases with the square of their separation.E = k|Q|/r²Electric field of a point chargeThe electric field created by an isolated point charge decreases with the square of the distance.V = kQ/rElectric potential of a point chargeElectric potential from a point charge varies inversely with distance and keeps the sign of the source charge.C = Q/VCapacitance, charge and voltageCapacitance tells how much electric charge a capacitor stores per volt across its terminals.E = ½CV²Energy stored in a capacitorA charged capacitor stores energy in its electric field. Stored energy grows with capacitance and with the square of voltage.Ceq: parallel ΣC; series 1/Σ(1/C)Capacitors in series and parallelEquivalent capacitance depends on the connection: capacitances add in parallel, while reciprocals add in series.τ = RCRC time constantThe time constant τ sets the characteristic charging and discharging timescale of an RC circuit.V₂/V₁ = N₂/N₁Ideal transformerFor an ideal transformer, the voltage ratio equals the turns ratio. More secondary turns increase voltage; fewer turns decrease it.

Waves & optics

Sound, refraction and optical quantities

v = fλWavelength, frequency and wave speedCalculate wavelength, frequency or wave speed from v = fλ.f = 1 / TFrequency and periodConvert between frequency and period using f = 1/T.n = c / vRefractive index calculatorCalculate refractive index from the speed of light in vacuum and the speed in a medium, or solve for the speed in the medium.n₁ sin θ₁ = n₂ sin θ₂Snell’s law calculatorSnell’s law relates the direction of a light ray before and after crossing the boundary between two transparent media.sin θc = n₂/n₁Critical angle for total internal reflectionTotal internal reflection becomes possible when light travels from a higher refractive index to a lower one. The critical angle is the incidence angle that would refract to 90°.P = 1/fOptical power and focal lengthOptical power is the reciprocal of focal length in metres. A shorter focal length means a larger magnitude of optical power.β = 10 log₁₀(I/I₀)Sound level and intensityThe decibel scale is logarithmic: a 10 dB increase corresponds to ten times the sound intensity.

Thermal physics

Heating, phase changes and expansion

Q = mcΔTHeat transfer: Q = mcΔTCalculate heat transferred during a temperature change without a phase change.ΔL = αL₀ΔTLinear thermal expansionA solid usually expands when its temperature rises. For modest temperature ranges, the change in length is approximately proportional to original length and temperature change.Q = mLLatent heatDuring an ideal phase change at constant temperature, energy can be absorbed or released without changing temperature.λmax T = bWien’s displacement lawFor an ideal blackbody, the wavelength at which emission peaks shifts toward shorter wavelengths as temperature rises.

Modern physics

Photons, matter waves and radioactivity

E = hc/λPhoton energyPhoton energy is proportional to frequency and inversely proportional to wavelength.λ = h/pde Broglie wavelengthMatter has wave properties: a particle with momentum p is associated with a de Broglie wavelength λ.N = N₀·2^(−t/T½)Radioactive decayRadioactive decay reduces the number of undecayed nuclei by half during each half-life.T½ = t·ln2 / ln(N₀/N)Half-life calculatorIf you know how much of a radioactive population remains after a measured time, you can infer its half-life from the exponential decay law.E = mc²Mass–energy equivalenceMass corresponds to an enormous amount of rest energy because the speed of light is squared.

Gravitation & space

Gravity, orbits and escape speed

F = Gm₁m₂/r²Universal gravitationNewton’s law of universal gravitation gives the magnitude of the attraction between two point masses, or spherical masses treated from their centres.v = √(GM/r)Circular orbital speedFor a circular orbit around a much more massive body, gravity supplies exactly the centripetal acceleration required for the orbit.vesc = √(2GM/r)Escape speedEscape speed is the minimum initial speed needed in the ideal two-body model to reach infinitely far away with zero remaining speed.T = 2π√(r³/GM)Circular orbital periodThe period of a circular orbit follows directly from gravity and circular motion.