Seven constants, seven working formulas, one slider. Press g, c, h, G, R, ke or v, move the single control, and watch the quantity that constant governs respond — with a logarithmic ruler above showing where each number sits on a scale spanning some 44 powers of ten.
The seven buttons do not just swap a number. Each one loads a different working formula, and the panel rebuilds around it: the equation on the headline readout, the constant's own value and status, and a line naming everything being held fixed. Under G that fixed setup is two 1000 kg masses; under ke it is two 1.0 microcoulomb charges; under R it is one mole of gas at one atmosphere. Those quantities are printed as text rather than offered as extra dials, so nothing competes with the one control you are actually moving. If you want to see how the same equations look when they are rearranged for a different unknown, the physics formulas cheat sheet lays them out side by side.
That is also why the slider's units change under you. It is never a generic dial — it is whatever the active formula takes as its single free input: kilograms under g, nanometres under h, kelvin under R, metres of separation under G and ke, degrees Celsius under the speed of sound. Under c the slider turns logarithmic as well, because the distance it has to cover runs from a kilometre out past the Sun, and a linear track would bury everything closer than a planet in the first pixel. Drag it out to about 1.5e11 m and the crossing time lands near 500 seconds, which is the eight-minute figure quoted in every account of how fast light travels.
The ruler along the top exists because these numbers cannot share an ordinary axis. The Planck constant sits at roughly 1e-34 and the Coulomb constant at nearly 1e10, so on a linear scale six of the seven would collapse onto the left-hand edge and read as zero. On the logarithmic ruler each factor of ten gets equal width, and the distance between the marks becomes the real story: the gap between G and ke is about twenty decades, which is exactly why two microcoulombs of charge overpower two tonnes of mass without difficulty.
The misconception the lab is built to kill is the one between g and G. They look like the same letter and get used almost interchangeably in conversation, but g is a local acceleration of 9.81 m/s² at the surface of this planet, printed alongside the Moon's 1.62 and Mars' 3.72 for comparison, while G is a universal constant in units of N·m²/kg² that appears in the law of gravitation anywhere in the universe. Select them one after the other and the difference is unmissable: different formula, different units, different picture. When you want to run G on your own pair of masses rather than the fixed pair here, the gravitational force calculator takes any two masses at any separation.
Because the slider is not a generic dial: it is whatever the active formula takes as its one free input. Under g that is a mass in kilograms, because weight is mass times g. Under h it is a wavelength in nanometres, because the photon energy is h times c divided by the wavelength. Under R it is a temperature in kelvin, under G and ke it is a separation in metres, and under the speed of sound it is the air temperature in degrees Celsius. Everything else in each formula is held fixed and printed as text below the slider, so there is only ever one thing moving and one result to watch.
Because the seven numbers span about 44 powers of ten. The Planck constant is roughly 6.6 followed by 34 decimal places of nothing, and the Coulomb constant is nearly nine billion. On an ordinary ruler where the Coulomb constant sat at the far right, every other constant on the page would be stacked invisibly on the left-hand edge, all of them indistinguishable from zero. A logarithmic ruler gives every factor of ten the same width, so each constant gets a visible place of its own and the enormous gaps between them become something you can actually see.
Because both force laws in this lab are inverse-square: the separation appears squared in the denominator, so doubling it does not halve the force, it quarters it. Ten times the distance means one hundredth of the force. That is why the two gravitational masses lose almost all their pull within the first metre of the slider's travel, and why the arrows between the two charges collapse so quickly. The panel keeps the exact figure in view while the picture shrinks, so you can check that the drop really is following one over r squared.
Three of them: c, h and R. Since the SI redefinition of 2019, c and h are fixed numbers by definition, and the metre and the kilogram are derived from them rather than the other way round. R is exact too, because it is the Avogadro constant multiplied by the Boltzmann constant and both of those are now defined. G is still measured, and badly: its uncertainty is around 22 parts per million, which makes it the worst-known constant here by a wide margin. The Coulomb constant is measured but known far more precisely, and the speed of sound is not a constant at all.
Partly as a contrast, and partly because it is the number most often mistaken for a universal constant. Standard gravity, g, is a local acceleration of about 9.81 metres per second squared at the surface of this particular planet; it changes with altitude and latitude and it is completely different on the Moon or Mars, which is why the g panel prints all three. The gravitational constant G is the universal one that appears in the law of gravitation everywhere in the universe. Selecting g and then G back to back is the fastest way to see that they are not the same quantity, are not measured in the same units, and cannot be substituted for one another.