u ↔ g Converter (per Particle)

Convert between atomic mass units (u) and grams per particle. Perfect for linking microscopic masses to macroscopic units using Avogadro’s number.

Background

The atomic mass unit (u) is defined so that 1 u equals one twelfth of the mass of a ¹²C atom. In practical chemistry, 1 u is numerically equivalent to 1 g/mol. Using Avogadro’s number (N_A = 6.02214076×10²³ mol⁻¹), we can convert u ↔ grams per particle directly.

How to use this converter

1) Pick the direction (u → g per particle, or g per particle → u).
2) Enter the numeric value.
3) Click Convert to see the answer and steps.
4) Use Swap to flip directions while keeping the value.

Why it works (the short version)

Definition: 1 u = 1 g/mol (numerically). A single particle has mass in grams that is its u value divided by N_A.
Exact constant: N_A = 6.02214076×10²³ mol⁻¹ (defined).
Useful identity: 1 u = 1.66053906660×10⁻²⁴ g (CODATA).

Formulas Used

Let N_A be Avogadro’s number.

m (g/particle) = \frac{m}{(u)} \div N_{A}

Equivalently, using the exact conversion:

m_{g} = m_{u} \times 1.66053906660 \times 10^{- 24}

Reverse direction:

m (u) = m (g/particle) \times N_{A}

Example Problems & Step-by-Step Solutions

Example 1

Convert 18.015 u (one H₂O molecule) to grams per molecule.

Use 1 u = 1.66053906660×10⁻²⁴ g.
m = 18.015 × 1.66053906660×10⁻²⁴ g ≈ 2.989×10⁻²³ g.

Example 2

Convert 3.0×10⁻²³ g per particle to u.

m(u) = m(g/particle) × N_A = 3.0×10⁻²³ × 6.02214076×10²³.
m(u) ≈ 18.07 u.

Frequently Asked Questions

Q: What’s the difference between u and g/mol?

Numerically, the values match: an atom with mass 12.011 u has a molar mass of 12.011 g/mol. The units are different (microscopic vs per mole).

Q: Why does 1 u equal 1 g/mol numerically?

By definition, 1 u is 1/12 of a ¹²C atom and Avogadro’s number is fixed, so the numbers align.

Q: Should I use significant figures?

Yes—match your given data. The default display shows ~6 decimals; adjust as needed.