How Do You Weigh Something Without Knowing What a Kilogram Is? Compare It

A spring scale measures force, so it responds to the pull of gravity on an object and gives a reading that depends on where it is used, being different at the poles, at altitude and on another planet. A balance compares two objects in the same gravitational field, so whatever gravity is, it acts equally on both sides and cancels out, which means the comparison holds anywhere. The instrument therefore answers a different and more robust question, namely whether one quantity of matter exceeds another, and it does so without needing to know what either weighs. That is why the balance was the standard instrument for precise work until electronic methods arrived.

Accuracy depends on a small number of physical properties:

• •A pivot with almost no friction, historically a knife edge on a hard flat surface
• •Arms of equal length, since any difference produces a systematic error
• •A centre of gravity slightly below the pivot, which sets the restoring force
• •A long light pointer, which magnifies a small tilt into a visible movement
• •Low mass in the beam itself relative to the loads
• •Shelter from draughts, vibration and temperature differences across the arms

Any real instrument has arms that differ slightly, which introduces an error, and there is an elegant method that removes it entirely without measuring the difference. The object is placed in one pan and balanced against sand or shot rather than against weights. The object is then removed and standard weights are added to the same pan until balance is restored against the same counterpoise. Whatever the arm lengths are, the weights and the object produce the same effect from the same position, so they are equal in mass. The method is named after Borda, was described in the eighteenth century, and remains the standard way of eliminating that class of error.

Several instruments answer the weighing question differently and the differences matter in practice. A steelyard uses one arm far longer than the other with a sliding counterweight, so a small weight balances a large load and the reading comes from the position rather than from matching masses, which suits markets and does not suit precise work. A spring scale measures the extension of a spring and is cheap, portable and dependent on local gravity, temperature and the spring not having aged. A load cell measures the tiny deformation of a metal element electrically and is what lies inside almost every modern scale from a bathroom to a weighbridge. Hydrostatic weighing determines density rather than mass, by weighing an object in air and again submerged.

Electronic balances now dominate and they work on a different principle, using an electromagnetic force to hold a pan in a fixed position and reporting the current required, which is fast, direct and readable to a great many digits. Those instruments still depend on comparison underneath, since they must be calibrated against known masses and must be recalibrated whenever they are moved, precisely because they respond to local gravity. The standard kilogram itself was a physical object until 2019, and every mass measurement in the world traced back through a chain of comparisons on balances to that one cylinder. Since the redefinition it traces to a fixed constant of nature instead, realised through an instrument that balances a mass against an electromagnetic force.

Comparing two objects in the same gravitational field cancels gravity out, so the result holds anywhere, unlike a spring scale which measures force and reads differently at different places. Sensitivity depends on a near-frictionless pivot, equal arms and a low centre of gravity. Substituting standard weights for the object against the same counterpoise removes arm-length error entirely, and electronic instruments still rely on comparison for calibration.