How to convert kilogram to atomic mass unit?

When dealing with scientific measurements, it is common to switch between different mass units, especially between the kilogram (kg)—the SI base unit of mass, and the atomic mass unit (amu)—the standard unit used for atomic and molecular masses. Converting between these units is essential for understanding how macroscopic quantities relate to the microscopic world of atoms and molecules.

This guide explains in detail how to convert kilograms (kg) to atomic mass units (amu), providing clarity with formulas, examples, and practical applications.

Basic Definitions

Conversion Factor Between Kilogram and Atomic Mass Unit

The key to conversion lies in understanding the exact value of the atomic mass unit in kilograms.

By definition:

1 amu = 1.66053906660 × 10⁻²⁷ kg

From this, we can derive the conversion relationship:

1 kg = 1 ÷ 1.66053906660 × 10⁻²⁷ amu ≈ 6.02214076 × 10²⁶ amu

This number is closely related to Avogadro’s constant because 1 mole of atomic mass units = 1 gram, and hence 1 kg = 1000 grams = 6.022 × 10²⁶ amu.

Conversion Formula

To convert kilograms to atomic mass units (amu), use the following formula:

Number of amu = Mass in kilograms ÷ (1.66053906660 × 10⁻²⁷)

Or equivalently: amu = kg × 6.02214076 × 10²⁶

Worked Example 1: Convert 0.001 kg to amu

Step 1:
Mass = 0.001 kg (which is 1 gram)

Step 2:
Number of amu = 0.001 kg ÷ 1.66053906660 × 10⁻²⁷ kg/amu

Step 3:
= 6.02214076 × 10²³ amu

Answer:
1 gram = 6.022 × 10²³ amu
which is consistent with Avogadro’s number.

Worked Example 2: Convert 2 kg to amu

Step 1:
Mass = 2 kg

Step 2:
amu = 2 × 6.02214076 × 10²⁶

Step 3:
amu = 1.204428152 × 10²⁷ amu

Answer:
2 kilograms = 1.204 × 10²⁷ amu

Why Is This Conversion Important?

• Bridge Between Scales: Allows scientists to compare bulk materials (kg) with atomic-scale particles (amu).
• Nuclear Calculations: Essential in nuclear physics and high-energy experiments.
• Material Science: Helps in nanotechnology to relate bulk properties with atomic-level properties.
• Mole Concept Mastery: Shows how kilograms, grams, moles, and amu are interrelated through Avogadro’s number.

Conversion Chart