On the left, under two glass bell jars, stands a platinum-iridium cylinder — the old kilogram standard. On the right, the copper coil of a Kibble balance moves up and down between the poles of a magnet. Current runs to it along the wires, and below it trembles the laser beam that measures its speed. The letters kg show through the scene. The display reads 1.000 000 00 kg. A recording light blinks.
Quantity data sheet
SI base unitrev. 2026-10Kilogram kg
SI base unit · quantity: mass
For a hundred and thirty years the kilogram was a single cylinder
In a vault near Paris, under three glass bell jars, lay a cylinder of platinum and iridium 39 mm high and 39 mm across. From 1889 its mass was the kilogram by definition. Once every few decades it was taken out to be compared with copies from different countries.
The copies and the standard turned out to drift apart: over a century the difference grew to about 50 micrograms — the mass of a grain of sand. Whether the copies or the standard itself was changing could not be known, because by definition the standard weighed exactly one kilogram.
Since 2019 the kilogram has been fixed through the Planck constant h = 6.626 070 15·10⁻³⁴ J·s. The link to mass comes from the Kibble balance: on it the weight of a mass is balanced by an electromagnetic force, and the current and voltage are measured through quantum effects that involve h. Now the kilogram can be realized in any laboratory.
The symbol is lowercase kg, both letters lowercase. Capital K is the kelvin; “Kg” and “KG” are wrong. The kilogram is the only SI base unit with a prefix in its name, so multiples are built from the gram: mg, Mg, not µkg or kkg. Mass is written with a lowercase m.
Mass and weight. The mass of a weight in kilograms is the same on Earth and on the Moon. Weight is the force with which it presses on its support, and it is measured in newtons. On the Moon the same weight weighs six times less. Household scales show mass but compute it from weight, so they are slightly off from city to city.
01 · Definition
Kibble balance · weight · massThe Kibble balance works in two steps. First a mass is placed on one pan, and the coil in the magnetic field is fed with a current so that it pulls upward with the same force. The weight of the mass, m·g, equals the electromagnetic force B·L·I.
Then the mass is removed and the coil is moved through the same field at a constant speed v. A voltage U = B·L·v is induced in it. The unknown product B·L cancels, leaving m·g·v = U·I. Mechanical power equals electrical power.
The voltage is measured with the Josephson effect, the current with the Hall effect. Both standards rest on the Planck constant. The acceleration of free fall g is measured by a gravimeter in the same room, the speed by a laser interferometer. So the mass of the weight comes from h, the second and the metre.
How to weigh a mass with current
A mass sits on the left pan; on the right, a copper coil hangs above a magnet. Set the mass and choose a place: at the equator gravity is weaker, at the pole stronger. The “Weigh” button switches on the current: a controller adjusts it until the beam is level. “Move” takes the mass off and pulls the coil through the field, inducing a voltage in it. From the two steps the instrument computes the mass. Blue shows the magnet and field, copper the coil, gold the current and power, red the tilt of the beam. Below are three views. “Balance” shows the forces on the beam during a step. “Standard drift” shows how the copies of the old cylinder drifted. “Mass and weight” shows the weight of the same mass in newtons in different places.
Gravity differs even within one city
At the pole g ≈ 9.832 m/s², at the equator ≈ 9.780 m/s²: the Earth is flattened and rotating. On a mountain top g is smaller, over dense rock larger. A Kibble balance compares forces, so without an exact local g it would be off by hundredths of a percent. Next to it there is always an absolute gravimeter, which drops a corner reflector in vacuum and measures its acceleration with a laser.
02 · Conversion
units · weight · energyFrom kilograms to grams, pounds and newtons
Enter a mass in any unit. The first tab converts it to kilograms, grams, tonnes, pounds, ounces and carats. The second shows the weight of this mass on the Earth, the Moon and Mars. The third gives its energy by E = m·c² and its frequency by h.
| {k} | {v} | {note} |
The mass of the electron is 9.1·10⁻³¹ kg, the mass of the Sun 2·10³⁰ kg. Sixty orders of magnitude lie between them. The kilogram sits almost in the middle — the mass of a litre of water, something easy to hold in your hand.
04 · Measuring instruments
comparator · weight · sphere · gravimeterMass is compared, not measured directly
{title}
{text}
05 · Writing rules
kg in lowercase · prefixes on the gramPrefixes go on the gram, not on the kilogram
The kilogram is written in lowercase, kg, with a space after the number. Multiples and submultiples are formed from the gram: mg, µg, Mg. The tonne, t = 1000 kg, is accepted for use with the SI. Weight is written in newtons.
Capital K is the kelvin. Two prefixes in a row are not allowed, so “mkg” and “kkg” are wrong. Weight is a force; its unit is the newton, not the kilogram. “µkg” is the same mistake with two prefixes; the correct form is mg. “Kilo” is a colloquial shortening; in text it is written in full.
06 · Neighbouring units
mass and forceWeight: 1 kg weighs 9.81 N.
Platinum-iridium — 21 500.
0.2 g — small masses of gemstones.
07 · Historical section
archive · from a litre of water to the Planck constantHow the kilogram was taken off the shelf
{title}
{text}
A standard that could not be checked
As long as the kilogram was an object, its mass equalled one kilogram by definition. If the cylinder lost atoms in cleaning or picked up dust from the air, the kilogram “changed” with it all over the world. This could be noticed only through the copies — and the copies were changing too.
In the verifications of 1946 and 1989 most national copies turned out heavier than the standard by a few tens of micrograms. On the right is how the masses of the copies drifted relative to the standard: the curves spread apart, while the standard itself always stays at zero.
The new definition removed this paradox. The cylinder is now an ordinary weight; its mass is known to about 10 µg and may change, while the kilogram stays the same.
Catalogue of quantities
Mass and weight · 12 unit sheets
Index · all quantities on one pageThe lab at the entrance to the indexA drop of acid changes the colour of the juice, salt colours the flame, water freezes at a tap. Below them are all Simetrium sheets, by discipline and alphabetically.Open the index →
