Planck Units Calculator
Express a length, time, mass, energy or temperature in Planck units — the natural scales built from G, c, ħ and k — and see the five Planck units themselves and what they mean.
Combine the gravitational constant, the speed of light and Planck's constant and only one length comes out: 1.
How the planck units calculator works
Combine the gravitational constant, the speed of light and Planck's constant and only one length comes out: 1.6 × 10⁻³⁵ meters. Likewize one time, one mass, one energy and one temperature. They are the scales at which quantum mechanics and gravity are equally important and no current theory works. In these units every fundamental constant is 1, which is why theorists use them.
A meter is 6 × 10³⁴ Planck lengths; a second, 2 × 10⁴³ Planck times; a proton, 8 × 10⁻²⁰ Planck masses — the Planck mass is the odd one out, being the mass of a flea's egg.
Formula: l_P = √(ħG/c³); t_P = l_P/c; m_P = √(ħc/G); E_P = m_P c²; T_P = E_P/k
Worked examples
| Inputs | In Planck units | Note |
|---|---|---|
| One meter | 6.1871e+34 Planck lengths | 6.2 × 10³⁴ Planck lengths |
| A proton's mass | 7.6850e-20 Planck masses | 7.7 × 10⁻²⁰ Planck masses |
| One second | 1.8549e+43 Planck times | 1.9 × 10⁴³ Planck times |
FAQFrequently asked questions
What are Planck units?
The natural units built from G, c, ħ and Boltzmann's constant alone. Max Planck proposed them in 1899 as units "independent of special bodies or substances".
Why do they matter?
They mark the scale where quantum gravity would be needed: a Planck length of 10⁻³⁵ m and a Planck energy of 10¹⁹ GeV, some fifteen orders of magnitude beyond any accelerator.
Why is the Planck mass so ordinary?
It is 22 micrograms — a grain of dust. It is the mass whose Compton wavelength equals its Schwarzschild radius, which is why a black hole lighter than it cannot be described classically.
Do theorists really set constants to 1?
Yes — in Planck units G = c = ħ = k = 1, and equations shed their constants. Converting back to SI at the end is what this page does.
Is the Planck length the smallest length?
Nobody knows. It is the length below which our theories stop making sense, which is not the same as space being grainy there.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.