Science calculators and simulators
Interactive calculators and simulators for understanding physics, astronomy, chemistry and biology by playing with the numbers. Each tool comes with an explanation, a step-by-step worked example and an FAQ. They were all built to explain the science of the novel Project Hail Mary, but you can use them without having read it.
Spaceflight and relativity
Time dilation calculator
Work out how much time slows down on a relativistic ship using the Lorentz factor, with trips to Tau Ceti, Proxima Centauri and Andromeda.
Open →Rocket equation calculator
Work out how much fuel a rocket needs with the Tsiolkovsky equation, and compare chemical rockets with an engine that emits light.
Open →Hohmann transfer calculator
Work out the delta-v and travel time of a Hohmann transfer between Solar System planets, such as Earth to Mars.
Open →Space communication delay
How long a message takes to reach the Moon, Mars, Voyager 1 or Tau Ceti at light speed, and how long you wait for a reply.
Open →Artificial gravity calculator
Work out the artificial gravity of a spinning ship or station from its radius and revolutions per minute, including comfort and Coriolis effects.
Open →Photon propulsion calculator
Work out the force produced by emitting light in one direction (F = P/c) and the acceleration it gives a tiny object. Solar sails and photon rockets.
Open →Mechanics and energy
Pendulum period calculator
Work out the period of a simple pendulum with T = 2π√(L/g) and measure gravity with a string and a watch. Animated simulator for Earth, the Moon and more.
Open →Free-fall gravity calculator
Measure the acceleration due to gravity by dropping an object and timing the fall: g = 2d/t². Compare with Earth, the Moon and Jupiter.
Open →E = mc² calculator
Convert any mass to energy with E = mc² and compare it with a kWh, a ton of TNT or the Hiroshima bomb. Plain explanation and worked examples.
Open →Measuring mass without gravity
In weightlessness a scale is useless, but mass is still there as inertia. A center-of-mass simulator and how astronauts weigh themselves on the ISS.
Open →Light, heat and climate
Interactive electromagnetic spectrum
Sweep the electromagnetic spectrum from X-rays to radio waves and see what each region is, how much energy it carries and what it is used for.
Open →Infrared spectroscopy lab
Compare the infrared absorption spectra of CO₂, water, methane, ammonia and oxygen. This is how the atmospheres of other planets are studied.
Open →Radiative cooling in a vacuum
Simulate how a hot object cools in space, where it can only lose heat by radiating: P = σ·A·T⁴. Why it doesn't freeze instantly.
Open →Solar luminosity simulator
Simulate a gradual dimming of the Sun and its effect on Earth. Why 5% less sunlight would be enough to cool the planet by several degrees.
Open →Global cooling simulator
Link a drop in Earth's average temperature to its consequences, from an ice age to a snowball Earth. Based on past climate data.
Open →Global warming potential comparator
Compare how much methane, nitrous oxide and SF₆ warm the planet relative to CO₂, using global warming potential (GWP) over 20 and 100 years.
Open →Biology and chemistry
Predator-prey simulator (Lotka-Volterra)
Simulate how prey and predator populations oscillate with the Lotka-Volterra equations. Cycles, equilibrium and biological pest control.
Open →Life solvent comparator
Compare water, ammonia and methanol as solvents for life: liquid range, polarity, hydrogen bonding and cosmic abundance.
Open →Directed evolution simulator
Simulate how mutation and selection adapt a population to a new environment in a few generations. The technique behind the 2018 Nobel Prize in Chemistry.
Open →Math and signals
Angular size calculator
Work out an object's real size from its distance and the angle it spans: size = 2·d·tan(θ/2). Examples with the Moon and buildings.
Open →Base 10 to base 6 converter
Convert numbers between base 10 and base 6 instantly. Learn how positional number systems work with step-by-step examples.
Open →Fourier transform visualizer
Combine musical notes and see how the Fourier transform splits sound into its frequencies. A visual explanation without hard formulas.
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