Conventional mass ↔ true mass
Convert a weight’s true (vacuum) mass to its conventional mass, the mass of a standard of 8000 kg/m³ that balances it at 20 °C in air of 1.2 kg/m³, or back. Stainless steel barely moves; aluminium shifts by about −3 × 10⁻⁴.
Conventional mass · OIML D 28
v0.1.0 · 8000 kg/m³ · 1.2 kg/m³Conventional mass m_c999.999056 gm_c − m = -0.0009435 g (-0.9435 × 10⁻⁶ of m)
m_c = m(1 − ρ0/ρ)/(1 − ρ0/ρc) · ρ0 = 1.2 kg/m³ · ρc = 8000 kg/m³ · 20 °C
Test vectors for this tool
The reference cases this calculator is tested against on every change. Use them to check your own software. All test vectors · Download JSON
| ID | Inputs | Expected | Tolerance | Source |
|---|---|---|---|---|
| CM-01 | mass = 1, density = 7950 | 0.9999990564622429 kg | ± 1e-15 | OIML D 28:2004, Conventional value of the result of weighing in air, clause 4 and eq. (1): m_c = m(1 − ρ0/ρ)/(1 − ρ0/ρc), ρ0 = 1.2 kg/m³, ρc = 8000 kg/m³; hand arithmetic in 50 digits. |
| CM-02 | mass = 1, density = 8000 | 1 kg | ± 1e-15 | OIML D 28:2004, Conventional value of the result of weighing in air, clause 4: a weight of the reference density ρc = 8000 kg/m³ has m_c = m by definition. |
| CM-03 | mass = 1, density = 2700 | 0.9997055113822628 kg | ± 1e-15 | OIML D 28:2004, Conventional value of the result of weighing in air, eq. (1); clause 5 states the relative deviation is about −3 × 10⁻⁴ for aluminium. |
| CM-04 | conventionalMass = 1, density = 7800 | 1.0000038467456531 kg | ± 1e-15 | OIML D 28:2004, Conventional value of the result of weighing in air, eq. (1) solved for m: m = m_c(1 − ρ0/ρc)/(1 − ρ0/ρ); hand arithmetic in 50 digits. |
| CM-05 | mass = 1, density = 50 | OutOfRangeError | exact | Metrology Bench limit: no weight or weighed solid is less dense than 100 kg/m³ (densest element ≈ 22 600 kg/m³; limit 25 000). |
| CM-06 | conventionalMass = 0, density = 8000 | RangeError | exact | OIML D 28:2004, Conventional value of the result of weighing in air, eq. (1) applies to a body with mass. |
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