ℏ Physics

The toolkit

• Uncertainty calculatorAvailable

  Propagate uncertainties through any formula with a contribution budget and a Monte Carlo check, analyse repeated readings, weighted means and whether two results agree.

• Graphs and model fittingAvailable

  Weighted least-squares lines with gradient and intercept uncertainties, χ² and residuals; linearise power laws and exponentials or choose your own axes.

• Units, constants and dimensionsAvailable

  Convert across sixteen quantities, check the dimensions of an equation, prefixes and significant figures, and CODATA 2022 constants.

• MechanicsAvailable

  Constant-acceleration solver, projectiles with and without air resistance, collisions with restitution, circular motion and banking, and inclined planes.

• Gravitation and orbitsAvailable

  Circular and elliptical orbits around any Solar System body, escape speed, Kepler’s third law and Hohmann transfers.

• OscillationsAvailable

  Simple harmonic motion, the exact large-angle pendulum, damping regimes, resonance curves with phase, and coupled oscillators.

• Waves and opticsAvailable

  String and pipe modes, Doppler shifts for sound and light, lenses and mirrors with a ray diagram, diffraction patterns and Fresnel reflection.

• CircuitsAvailable

  Equivalent resistance of any network, a Kirchhoff solver, RC and RL transients, AC impedance and resonance, capacitors and wires.

• Electric and magnetic fieldsAvailable

  Field-line maps of point charges you place, charged particles in fields, fields of wires and coils, and induction.

• Thermal physicsAvailable

  Gas processes on a pV diagram, heat and phase changes, engine efficiencies, Maxwell–Boltzmann speeds, blackbody spectra and entropy.

• Quantum, nuclear and relativityAvailable

  Photons and the photoelectric effect, matter waves, Compton scattering, hydrogen spectra, particle in a box, special relativity, decay and binding energy.

• AstrophysicsAvailable

  Parallax, magnitudes and luminosity, stellar radii, black holes and a ΛCDM cosmology calculator.

• Derivation notebookAvailable

  Write derivations line by line in LaTeX with a reason for each step, typeset as you type, saved and printable.

• Lab and problem plannersAvailable

  Templates for experiment plans, lab reports, physics risk assessments and problem solving, saved and printable.