Physics calculators

Each tab is a set of small calculators: change any input and the results update. Inputs accept arithmetic (2*9.81, 6.371e6).

Constants — CODATA 2018 recommended values with standard uncertainties; values fixed by the 2019 SI are marked exact.
Kinematics — fill any three of s, u, v, a, t; the other two follow from the constant-acceleration equations. When a square root allows two answers, both are shown.
Projectile — range, flight time, and apex without drag, plus a numerical (RK4) trajectory with linear drag (F = −bmv) or quadratic drag (F = ½ρC_dAv²) plotted for comparison.
Oscillations — the pendulum period uses the exact large-amplitude formula T = T₀ / AGM(1, cos(θ₀/2)).
Forces — a block on an incline: whether static friction holds, the friction force, and the acceleration, with a free-body diagram. Circular motion from any of v, ω, or the period.
Energy & momentum — kinetic and potential energy, work and power, and 1-D collisions with a coefficient of restitution (1 elastic, 0 perfectly inelastic).
Waves & sound — v = fλ, the speed of sound with temperature, the Doppler effect (speeds positive when approaching), and decibel arithmetic.
Optics — the thin lens and mirror equation with a ray diagram (real is positive), Snell’s law with critical and Brewster angles, and the eye in dioptres (below).
Thermodynamics — Q = mcΔT, latent heat, the ideal gas law, thermal expansion, and Stefan–Boltzmann and Wien radiation.
Gravitation — circular orbits around Earth, the Moon, Mars, Venus, Jupiter, and the Sun, and Newton’s law of gravitation.

Material constants (specific heats, expansion coefficients, refractive indices) are typical room-temperature values.

⛶ Full screen (or F) gives the drawing on the open tab — the projectile trajectory, the ray diagram or the free-body diagram — the whole screen, with its inputs and results below it. It uses the browser’s full screen where it is allowed, otherwise a full-window layer (iPhone), and is redrawn as the window changes. Escape leaves.

The eye in dioptres

Educational — not a medical device. Not for diagnosis, treatment, monitoring or dosing. Toy model — not physiology.

At the bottom of the Optics tab (open it), optical power P = 1/f (dioptres, f in metres) applied to the eye:

Far point of an uncorrected eye from its distance refraction: a −2.0 D myope sees clearly out to 1/2.0 = 0.5 m. A long-sighted (+) eye has no far point in front of it; it must accommodate even for distance.
Accommodation amplitude by age, from the book’s orientation figures — about 10 D at 20, 4–6 D at 40, about 1 D by 60 — interpolated as a range between them. Ages outside 20–60 are refused rather than extrapolated, because the book gives no figures there.
Near points (uncorrected, and with the distance correction worn), and the reading add by the book’s arithmetic: focusing demand 1/d minus the accommodation available. A 60-year-old with about 1 D reading at 40 cm needs 2.5 D; the eye supplies 1, so +1.5 D. This is arithmetic, not a prescription — eye-care practice also keeps some accommodation in reserve, measures rather than assumes, and accounts for vertex distance, all of which this ignores.
Eye length: each extra millimetre of axial length adds roughly 2.5–3 D of myopia.

Companion to chapter 8, “The head and neck: eye, ear, nose, throat, and mouth” of Human Biology for the Medical Maker. All the eye figures above come from that chapter.

Share link (under the title) copies a URL that reopens this tool exactly as you have it — every tab’s inputs, with the current tab selected. Opening such a link replaces the inputs this browser had saved for the tool.

Related: spectrum analyser (with synthetic biosignals), unit converter.

The eye in dioptres

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