Kilogram to Planck Mass Converter
Quickly convert from Kilogram to Planck Mass.
How to convert
Formula:
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At the atomic and subatomic scale, the kilogram is far too large to be practical.
Where is it used?
• Molecular Biology and Biochemistry — Protein and nucleic acid masses are expressed in daltons (Da) or kilodaltons (kDa); haemoglobin ~64,500 Da (64.5 kDa); the ribosome ~2,500 kDa; mass spectrometry identifies...
Examples:
• 1 unified atomic mass unit (u / Da) = 1.66054 × 10⁻²⁷ kg
• 1 electron mass (mₑ) = 9.10938 × 10⁻³¹ kg = 0.000549 u
At the atomic and subatomic scale, the kilogram is far too large to be practical. Physicists and chemists use the unified atomic mass unit (u or Da, also called the dalton), defined as exactly 1/12 the mass of a carbon-12 atom: 1 u = 1.66054 × 10⁻²⁷ kg. Subatomic particle masses — electron, proton, neutron — are given in atomic mass units or in MeV/c² via Einstein's mass-energy equivalence. The Planck mass (~21.8 μg) is the natural mass scale of quantum gravity.
The unified atomic mass unit u (dalton, Da) is the standard mass unit in atomic physics, chemistry, and biochemistry. Relative atomic masses of elements are dimensionless ratios relative to u, e.g., carbon-12 = 12 u exactly. Key particle masses: electron mₑ = 9.10938 × 10⁻³¹ kg = 0.000549 u = 0.511 MeV/c²; proton mₚ = 1.67262 × 10⁻²⁷ kg = 1.007276 u = 938.3 MeV/c²; neutron mₙ = 1.67493 × 10⁻²⁷ kg = 1.008665 u = 939.6 MeV/c². The Planck mass mP = √(ℏc/G) ≈ 2.176 × 10⁻⁸ kg (~21.8 μg).
Where is it used?
- Molecular Biology and Biochemistry — Protein and nucleic acid masses are expressed in daltons (Da) or kilodaltons (kDa); haemoglobin ~64,500 Da (64.5 kDa); the ribosome ~2,500 kDa; mass spectrometry identifies biomolecules by their mass-to-charge ratio (m/z) in Da.
- Nuclear and Particle Physics — Particle masses are expressed in MeV/c² (using E = mc²): electron 0.511 MeV/c², proton 938.3 MeV/c², Higgs boson 125,100 MeV/c². Nuclear binding energy calculations use atomic mass units to find mass defects.
- Chemistry and the Mole Concept — The molar mass of a substance in g/mol is numerically equal to its relative molecular mass in u: water (H₂O) = 18.015 u per molecule = 18.015 g/mol. This equivalence is the foundation of stoichiometry.
- Mass Spectrometry — Mass spectrometers measure mass-to-charge ratio in thomson (Th) = u/elementary charge; instruments resolve isotopes differing by 1 u, and high-resolution instruments achieve sub-mDa mass accuracy for molecular formula determination.
Common Conversion Mistakes
Confusing atomic mass unit (u) with gram per mole (g/mol)
1 u is the mass of a single atom in atomic mass units; 1 g/mol is the molar mass — the mass of one mole (6.022 × 10²³) of those atoms in grams. Numerically they are equal (carbon-12: 12 u per atom, 12.000 g/mol) but dimensionally different. Treating u and g/mol as the same unit in a formula that mixes per-atom and per-mole quantities produces errors of a factor of Avogadro's number (6.022 × 10²³).
Assuming the proton and hydrogen atom masses are equal
The hydrogen atom mass (1.007940 u) includes the proton (1.007276 u) plus the electron (0.000549 u) minus the electron binding energy (13.6 eV ≈ 1.46 × 10⁻⁸ u, negligible). For most purposes they are close, but in precise nuclear mass calculations and binding energy determinations, the distinction matters. Atomic mass tables give atomic masses (including electrons), not nuclear masses.
Using dalton and atomic mass unit as if they were defined differently
The dalton (Da) and the unified atomic mass unit (u) are exactly the same unit: 1 Da = 1 u = 1.66054 × 10⁻²⁷ kg. 'Dalton' is the name preferred in biological sciences and mass spectrometry; 'atomic mass unit' or 'u' is preferred in physics and chemistry. Some older literature uses 'amu' to refer to the older oxygen-based standard (where ¹⁶O = 16 exactly), which differs from the modern carbon-12 based definition by about 275 ppm.
Treating MeV/c² as a unit of energy rather than mass
MeV/c² is a unit of mass via E = mc², not a unit of energy. The 'MeV' part often causes confusion: saying the electron has a mass of 0.511 MeV is informal shorthand and technically incomplete — the proper unit is 0.511 MeV/c². Keeping the /c² explicit helps prevent dimensional mistakes in momentum-energy-mass relationships.
Quick Reference Table
| From | To |
|---|---|
| 1 unified atomic mass unit (u / Da) | 1.66054 × 10⁻²⁷ kg |
| 1 electron mass (mₑ) | 9.10938 × 10⁻³¹ kg = 0.000549 u |
| 1 proton mass (mₚ) | 1.67262 × 10⁻²⁷ kg = 1.007276 u |
| 1 neutron mass (mₙ) | 1.67493 × 10⁻²⁷ kg = 1.008665 u |
| 1 Planck mass (mP) | 2.17643 × 10⁻⁸ kg (~21.76 μg) |
| 1 MeV/c² | 1.78266 × 10⁻³⁰ kg = 0.001074 u |
| Mass of carbon-12 atom | 12.000 u (by definition) |
Frequently Asked Questions
What is the unified atomic mass unit (dalton)?
The unified atomic mass unit (u), also called the dalton (Da), is defined as exactly 1/12 the mass of a carbon-12 atom in its ground state. Its SI value is 1 u = 1.66053906660 × 10⁻²⁷ kg (CODATA 2018). The 'unified' designation distinguishes it from the older oxygen-based standard. It was adopted in 1961 and is the basis of all relative atomic and molecular mass scales used in chemistry and biochemistry today.
Why are particle masses given in MeV/c²?
Einstein's equation E = mc² relates mass and energy. In particle physics, energies are measured in electron volts (eV) or megaelectron volts (MeV), so masses are expressed in MeV/c² — the mass that has rest energy 1 MeV. This is convenient because particle accelerators measure energies directly: the electron has rest energy 0.511 MeV, so its mass is 0.511 MeV/c². Conversions: 1 MeV/c² = 1.78266 × 10⁻³⁰ kg; proton = 938.272 MeV/c².
How is the dalton used in protein science?
Protein mass is the sum of the atomic masses of all constituent atoms (in daltons), minus the water molecules lost during peptide bond formation. A protein of 100 amino acids has a typical mass of ~11,000 Da (11 kDa). Modern mass spectrometry can measure protein masses to ppm accuracy. Kilodalton (kDa) and megadalton (MDa) are common: antibody IgG ≈ 150 kDa; the nuclear pore complex ≈ 120 MDa. Gel electrophoresis separates proteins by mass using kDa ladder standards.
What is the Planck mass and why is it important?
The Planck mass mP = √(ℏc/G) ≈ 2.176 × 10⁻⁸ kg ≈ 21.76 μg is the natural mass scale at which gravitational and quantum effects are equally important. It is far larger than any elementary particle — a proton is ~10¹⁹ times lighter than the Planck mass — but far smaller than anything macroscopic. A black hole with mass ~mP would have a Schwarzschild radius equal to the Planck length. Quantum gravity theories must describe physics near this scale, which is inaccessible to current experiments.
Sources & Standards
- CODATA 2018 Recommended Values of the Fundamental Physical Constants (NIST)
- IUPAC — Compendium of Chemical Terminology ('Gold Book'), 2nd ed. (1997, updated online)
- Particle Data Group — Review of Particle Physics, Progress of Theoretical and Experimental Physics (2022)
- BIPM — The International System of Units (SI), 9th edition (2019)
Reviewed by The Unit Hub Editorial Team · March 2026