Mass Converter
Convert mass across sixty orders of magnitude — from the electron and the atomic mass unit through slugs and hundredweight to Earth and solar masses — with exact factors and the weight distinction made explicit.
Mass Converter
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Astronomical and atomic masses are measured, not defined, and carry experimental uncertainty in their final digits.
- Planetary surface gravities used for the weight comparison are nominal mean values; real surface gravity varies with latitude and altitude.
- This engine covers the scientific scale — for everyday ounces, stones and the troy system use the Weight Converter.
- Relativistic mass increase is not modelled; all values are rest masses.
In short: Mass conversion routes through the kilogram, the SI base unit. This engine covers the scientific and engineering scale rather than the everyday one: the slug, the atomic mass unit, planetary masses and the archaic commercial units. Mass is invariant — it does not change with location. What changes is weight, which is a force, and which is converted on the Force Converter.
Formula
Each factor is the number of kilograms in one of that unit. Mass converts by ratio alone and is independent of location. Weight is a separate quantity entirely — the gravitational force on that mass — and it scales with the local value of g, which is why the same object weighs six times less on the Moon while its mass is unchanged.
Worked Example
- Identify the source factor. One slug is 14.593903 kg, derived as one pound-force divided by one foot per second squared.
- Convert to the base unit. 1 × 14.593903 = 14.593903 kg.
- Identify the target factor. One pound-mass is exactly 0.45359237 kg.
- Divide. 14.593903 ÷ 0.45359237 = 32.174049 lbm.
- Recognise the number. 32.174049 is gn expressed in feet per second squared — the slug is defined so that this is true.
Metrology note. Since 2019 the kilogram has been defined by fixing the Planck constant at exactly 6.62607015 × 10−34 J·s. The platinum-iridium prototype held at Sèvres was retired, ending the last physical artefact definition in the SI. The kilogram is now reproducible in any suitably equipped laboratory rather than being a lump of metal in a vault outside Paris.
Strengths & Limits Of This Model
Where this engine is strong
- Spans sixty orders of magnitude, from the electron to the Sun, in one table.
- Treats mass and weight as the distinct quantities they are, rather than conflating them.
- Every terrestrial factor is exact by treaty definition, not rounded.
- Flags which values are measured rather than defined.
Where it stops
- Deliberately omits the everyday commercial units, which live on the Weight Converter.
- Cannot express uncertainty ranges on the measured astronomical values.
Practical Use Cases
Engineering dynamics in US customary units
The slug is the mass unit that makes F = ma work without a conversion constant, because it is defined as the mass accelerated at one foot per second squared by one pound-force. Working in slugs eliminates the gc factor entirely — see the Force Converter for the force side of the same problem.
Atomic and molecular calculations
The atomic mass unit is one twelfth the mass of a carbon-12 atom, 1.66053907 × 10−27 kg. Converting between daltons and kilograms is routine when moving between molecular data and bulk quantities.
Astronomical scale comparisons
Solar and Earth masses are the working units of astrophysics because kilograms become unwieldy past about 1024. The orders-of-magnitude readout makes the span between atomic and stellar scales legible.
Reading historical commercial records
Hundredweight, quarters, pennyweight and scruples appear throughout older trade, apothecary and assay documents. The US hundredweight is 100 pounds while the UK hundredweight is 112 — a 12 per cent difference that has caused real disputes.
Methodology & Editorial Standards
Every factor is the exact number of kilograms in one unit of the source. The pound-mass is exactly 0.45359237 kg under the 1959 International Yard and Pound Agreement; the grain is exactly one seven-thousandth of that, 64.79891 mg, from which the pennyweight and scruple follow exactly. The slug is derived as the pound-force divided by one foot per second squared, giving 14.593902937206362 kg, which is 32.174049 pounds — numerically equal to standard gravity in feet per second squared, by construction. The atomic mass unit and electron mass are CODATA 2022 values. Planetary and solar masses are measured astronomical quantities. Astronomical and atomic masses are measured quantities, not definitions, and carry experimental uncertainty in their final digits. Every other factor on this page is exact. This engine deliberately carries the scientific and engineering scale; the everyday units of commerce, including the full troy system, are handled by the Weight Converter. All conversion factors are exact by definition under the International System of Units, or exact by international agreement where the unit is defined by treaty. Values are held at full IEEE-754 double precision internally and rounded only for display, so chained conversions do not accumulate drift.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Mass Converter — 10 Expert FAQs
10 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
What is the difference between mass and weight?
Mass is the amount of matter in an object and is invariant — it is the same everywhere in the universe. Weight is the gravitational force acting on that mass, so it changes with location. A 70 kg person has a mass of 70 kg on the Moon, but weighs about one sixth as much because lunar gravity is roughly 1.62 m/s² against Earth's 9.80665. Mass is measured in kilograms; weight, being a force, is properly measured in newtons.
What is a slug?
The slug is the mass unit of the US customary gravitational system, defined as the mass that accelerates at one foot per second squared under one pound-force. That works out to 14.593903 kg, or 32.174049 pounds-mass. Its purpose is to make Newton's second law work without a conversion constant: using slugs, F = ma holds directly, whereas using pounds for both mass and force requires the awkward gₑ factor.
Why is the same object 32.174 pounds and 1 slug?
Because the slug is defined to make it so. Standard gravity is 9.80665 m/s², which is 32.174049 ft/s². Defining the slug as one pound-force per foot per second squared forces the ratio between the slug and the pound-mass to equal that same number. The coincidence is deliberate engineering design, not an accident of measurement.
How is the kilogram defined now?
Since May 2019 the kilogram has been defined by fixing the numerical value of the Planck constant at exactly 6.62607015 × 10⁻³⁴ joule-seconds. Before that it was defined by a physical platinum-iridium cylinder kept near Paris, which was the last artefact definition in the SI and which was known to be drifting relative to its own official copies.
What is an atomic mass unit?
The atomic mass unit, also called the dalton, is defined as one twelfth of the mass of an unbound carbon-12 atom at rest in its ground state. That equals approximately 1.66053907 × 10⁻²⁷ kg. It is the natural unit for expressing atomic and molecular masses, since a carbon-12 atom is exactly 12 u by definition.
Is a US hundredweight the same as a UK hundredweight?
No, and the difference is substantial. The US hundredweight, sometimes called the short hundredweight or cental, is 100 pounds. The UK hundredweight, or long hundredweight, is 112 pounds — twelve per cent heavier. This follows through into the tons built from them: the US short ton is 2,000 pounds and the UK long ton is 2,240.
Why does this converter not have ounces and stones?
Because the Weight Converter already covers the everyday avoirdupois and troy scale in full, including ounces, stones, tons and the complete troy system for precious metals. This engine deliberately takes the scientific and engineering units that page omits, so the two complement each other rather than duplicating.
How precise are the astronomical masses?
Considerably less precise than everything else here. The Earth mass of 5.9722 × 10²⁴ kg and solar mass of 1.98892 × 10³⁰ kg are measured quantities limited by the precision of the gravitational constant G, which remains one of the least accurately known constants in physics. Treat them as good to about five significant figures, unlike the treaty-defined units which are exact.
What are pennyweights and scruples?
Both are grain-based subdivisions still met in specialist work. A pennyweight is 24 grains, one twentieth of a troy ounce, and is standard in jewellery and precious-metal assay. A scruple is 20 grains and comes from the apothecaries' system, appearing in historical pharmaceutical records. Both are exact, since the grain is exactly 64.79891 mg.
Why do very large and very small values switch to scientific notation?
Because fixed decimal notation stops being readable outside a fairly narrow band. An electron mass written out in full is a decimal point followed by thirty zeros. The scientific notation output shows every value in exponent form regardless, and the orders-of-magnitude figure gives the base-ten logarithm relative to one kilogram.