Physics
Physics calculators
Kinematics, energy and electricity: the calculations of the school physics course, with every derived quantity beside the headline result. From second-year physics: electrostatics, capacitors, magnetism, induction, AC circuits and electromagnetic waves. Plus fluids and thermodynamics: fluid statics and dynamics, calorimetry and heat engines.
Which calculation you need
Kinematics answers questions about distance, speed and time: uniform motion when the speed does not change, uniformly accelerated when the acceleration is constant, free fall and projectile motion for the two cases where the acceleration is that of gravity. There is also the time-free relation, v² = v₀² + 2as, which is the one to use when the problem gives both speeds and the acceleration but no seconds. Work and energy cover the next chapter, where motion is described in joules rather than metres per second: kinetic, gravitational and elastic potential energy, the work of a force with its angle, power and momentum. Electricity starts from Ohm's law and reaches the equivalent resistance of series and parallel networks, with the power dissipated and the voltage across each resistor. The electromagnetism of the second course starts from Coulomb's law and the electric field, moves through capacitors and the magnetic field produced by currents, reaches Faraday-Lenz induction and alternating-current circuits, where opposite reactances cancel at the resonant frequency. It closes with electromagnetic waves and wave optics: c = λf, photon energy, Snell's law and double-slit interference.
Motion and projectiles
Uniform and uniformly accelerated motion, free fall, braking and launch at an angle.
Dynamics and Newton's laws
Second law, weight, friction, inclined plane, centripetal force and impulse, with the formula inverting itself.
Collisions and momentum
Head-on collisions, elastic, inelastic and in between: final velocities, energy lost and impulse exchanged.
Rotational dynamics
Moment of inertia, the parallel axis theorem, torque, angular momentum and rolling, with the formula that rearranges itself.
Universal gravitation
Newton's law, surface gravity, orbital and escape speed, Kepler's third law and gravitational potential energy.
Oscillations and harmonic motion
Mass on a spring, simple pendulum, maximum speed and acceleration, oscillator energy and damping, with the motion plotted.
Error propagation
The uncertainty of a quantity computed from any formula, in quadrature and as a maximum error, and the mean of repeated readings with its error.
Linear regression
The least-squares line with the uncertainties of slope and intercept, weighted when you have σ, correlation coefficient and χ², with the plot.
Work, energy and power
Kinetic, gravitational and elastic potential energy, work of a force, power and momentum.
Ohm's law and resistance
Voltage, current, resistance and power dissipated, with series and parallel resistor networks.
Resistor colour code
Value and tolerance of a resistor from its colour bands, in 4, 5 or 6 bands.
Kirchhoff's laws
Resistivity, real sources, loops, junctions and voltage and current dividers.
Coulomb's law and the electric field
Force between charges, field, potential and electrostatic energy, with the formula reversible on every quantity.
Gauss's law
Electric flux, enclosed charge and the fields of a charged line, plane and sphere.
Capacitors
Capacitance, charge, voltage and energy, the parallel-plate capacitor and the equivalent capacitance in series and parallel.
Magnetic field and Lorentz force
Force on charges and wires, the field of a wire, a loop and a solenoid, radius of curvature and cyclotron frequency.
Electromagnetic induction
Flux, the Faraday-Lenz law, motional emf, the inductance of a solenoid and the energy in a coil.
RLC circuits and alternating current
Reactances, impedance, resonant frequency, power factor and the RC and RL time constants.
Poles and zeros
Roots of the numerator and denominator of H(s), the map in the s-plane and the stability verdict.
Bode plot
Magnitude and phase on a logarithmic scale, with the phase margin and the gain margin.
Pressure loss
Darcy–Weisbach and Colebrook–White: velocity, Reynolds, friction factor and the loss in metres, pascals and bar.
Voltage drop
The drop in volts and per cent along a cable, and the smallest section that stays inside the limit.
Beam bending
Moment, shear, stress and deflection for a simply supported or cantilever beam, with the diagrams.
Electromagnetic waves and optics
Wavelength and frequency, photon energy, Snell's law, intensity and interference fringes.
Refraction and Snell's law
Angle of refraction, critical angle and total internal reflection, with a draggable ray diagram.
Lenses and mirrors
Thin lens equation, spherical mirrors, magnification and dioptres.
Polarisation and diffraction
Malus's law, Brewster's angle, single slit, grating, Rayleigh and thin films.
Mechanical waves
Stretched strings, the speed of sound, Doppler, beats, decibels and harmonics.
Fluid statics
Stevin's law, hydraulic press, communicating vessels, buoyancy and apparent weight.
Fluid dynamics
Flow rate, continuity, Bernoulli, Torricelli, Venturi, Poiseuille and Reynolds.
Calorimetry
Sensible and latent heat, thermal equilibrium, expansion and conduction.
Thermodynamics
First law, transformations, adiabatics, efficiency, Carnot and entropy.