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Diffusion Coefficient Calculator

Ten times the distance takes a hundred times the time, which is why anything big needs a pump.

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Diffusion coefficient2.4537 × 10⁻¹⁰ m²/s2.4537 × 10⁻⁶ cm²/s
Distance covered in one second38.37 µmroot-mean-square, in three dimensions
In one millisecond1.2134 µm
In one hour2.3022 mm
Time to cross one millimetre679.24 sdistance goes as the square root of time
Time to cross one metre21.524 yearswhich is why circulatory systems exist
Ten times the distance takes a hundred times the time. Diffusion is excellent at cellular scale and hopeless above a millimetre or so, and that single fact sets an upper bound on how large an organism can be without a pump.

The formula

D = kB T / (6 pi eta r)

Bigger and thicker both slow it down

The Stokes-Einstein relation puts the diffusion coefficient inversely proportional to both the particle radius and the viscosity of the medium. Double the radius and diffusion halves. Warm the solvent and it speeds up twice over, because temperature appears in the numerator AND lowers the viscosity in the denominator — which is why the effect of heating on diffusion is larger than the bare factor of T suggests.

Diffusion does not scale with time

Distance grows as the square root of time, so covering ten times the distance takes a hundred times as long. A small molecule crosses a bacterium in about a millisecond and a human cell in a second, but would need years to cross a metre. This is precisely why anything larger than an insect needs a circulatory system: diffusion alone simply cannot deliver oxygen at that scale.

Where these models stop

Michaelis-Menten assumes a single substrate and a steady state; Langmuir assumes one layer on identical sites with no interaction between them; Stokes-Einstein assumes a hard sphere much larger than the solvent molecules around it. Each is an idealisation that happens to describe real systems well over a useful range, and each fails predictably outside it. Knowing which assumption a number rests on is usually more valuable than the number.