Kibble Balance: Weighing Mass with Planck's Constant

Phase

Setup

True test mass 1.000 kg

Magnetic flux density B 0.80 T

Coil current I 0.000 A

Live Readouts

Geometric factor B·L

160.0 T·m

Beam angle

0.0°

Induced voltage U

0.000 V

Net torque

0.00 N·m

Recorded I (weighing) / U (velocity)

— / —

Computed mass m = U·I / (g·v)

— kg

How it works

A Kibble (watt) balance measures mass without ever needing to know the exact magnetic field or coil geometry, by running the same coil in the same field through two phases and dividing them.

Weighing phase (static):
  m·g = B·I·L        → force balance

Velocity phase (coil moves at v):
  U = B·L·v          → induced EMF (Faraday's law)

Divide out the unknown geometric factor B·L:
  m·g·v = U·I
  m = U·I / (g·v)

The geometric factor B·L cancels exactly because both phases share the same coil sitting in the same field — it never has to be measured. All that remains is a current I, a voltage U, a velocity v and g.

Weighing phase — adjust coil current until the magnetic force B·I·L exactly nulls the weight of the test mass on the beam (Servo Null does this instantly); record that current.
Velocity phase — move the same coil through the field at a constant, precisely known velocity; record the induced voltage.
Combine — once both are recorded, m = U·I / (g·v) gives the mass.

Real Kibble balances read U and I from the two purest quantum electrical standards known: the Josephson effect gives a voltage locked to n·f·h/2e, and the quantum Hall effect gives a resistance locked to h/e² (so I = U_R/R). Both trace straight back to Planck's constant h and the electron charge e. Since the 2019 SI redefinition fixed the numerical value of h exactly, this chain runs in reverse at national metrology institutes: h is no longer measured from the kilogram — the kilogram is realized from h, and the Kibble balance is the instrument that does it.

WEIGHING PHASE

Coil / field region Test mass

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