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06 Numbers and Powers

Convert amu to kg: Formula, Calculator & Example

Card No. 06·60688 · Updated · Standard formula, shown below

The calculator on this card is switched off while it is checked. The formula is below, and the worked example shows how to do the sum by hand.

Convert atomic mass units (amu) to kilograms (kg) by multiplying the amu value by the mass of one atomic mass unit in kilograms. Enter a mass in amu to get its equivalent in kg, plus the conversion factor for reference.

Formula

The conversion formula is:

Mass in kilograms = mass in amu × 1.66053906660 × 10−27 kg/amu

  • Mass in amu is the number you enter, expressed in atomic mass units.
  • 1.66053906660 × 10−27 kg/amu is the conversion factor: one atomic mass unit is approximately this many kilograms.
  • Mass in kilograms is the converted result.

The atomic mass unit is also called the unified atomic mass unit, symbol u, and is often called a dalton, symbol Da. For this conversion, amu, u, and Da represent the same unit. The factor shown is the current defined value of the atomic mass constant expressed in kilograms; the calculator rounds its main result to six significant decimal places as a decimal display, which may show zero for extremely small inputs. Use scientific notation when you need to preserve the scale.

Worked Example

Using the calculator’s default input of 1 amu:

  1. Start with the conversion factor: 1.66053906660 × 10−27 kg/amu.
  2. Multiply the entered mass by the factor: 1 amu × 1.66053906660 × 10−27 kg/amu.
  3. Cancel amu in the units and multiply: 1.66053906660 × 10−27 kg.

The calculator’s main result is approximately 0.000000000000000000000000001661 kg when shown to six decimal places in the coefficient (equivalently, 1.660539 × 10−27 kg). The factor output is 1.66053906660 × 10−27 kg/amu.

What You’ll Need

  • The mass value you want to convert, in amu, u, or Da.
  • A calculator or spreadsheet if you are not using the converter above. Scientific notation is useful for handling the very small kilogram values.
  • The required precision for your calculation, such as a specific number of significant figures.

Step-by-Step

  1. Identify the input unit. Check that your value is in amu, unified atomic mass units (u), or daltons (Da). These are equivalent for this conversion. If your value is already in kilograms, do not convert it again.
  2. Enter the numerical mass. Type the value into the Mass field. Enter only the number; the unit is already specified. For example, if the value is 12 amu, enter 12.
  3. Multiply by the conversion factor. Use 1.66053906660 × 10−27 kg for every 1 amu. With 12 amu, the calculation is 12 × 1.66053906660 × 10−27 kg.
  4. Read the result in kg. The first output is the mass in kilograms. Since the result is tiny for ordinary atomic masses, express it in scientific notation rather than writing a long string of zeros.
  5. Keep appropriate precision. Carry enough digits through intermediate calculations, then round the final value to match the precision of the original data or your task. Do not assume that a long calculator display means the measured input was equally precise.
  6. Check the scale and units. A value of 1 amu is about 1.66 × 10−27 kg. If your result is near 10−27 kg for an input near 1 amu, the scale is plausible. A result near 1027 kg usually means the exponent or operation was reversed.

Common Mistakes

  • Dividing instead of multiplying. To convert amu to kg, multiply by 1.66053906660 × 10−27. Dividing by that factor is not the amu-to-kg operation.
  • Dropping the negative exponent. The factor is 1.66053906660 × 10−27, not 1.66053906660 × 1027. The negative exponent is essential because one atomic mass unit is an extremely small mass in kilograms.
  • Entering a value already converted. Confirm the input unit before using the factor. Multiplying a kilogram value by the factor again produces an incorrect result.
  • Rounding too soon. Keep the full factor during calculations. Rounding it to 1.66 × 10−27 can be fine for rough work, but it can affect results when high precision is required.
  • Confusing atomic mass with molecular mass. A molecule’s mass in amu is the sum of its constituent atoms’ masses. The conversion formula changes the unit; it does not determine the molecule’s composition or calculate its mass from a chemical formula.

Tips

  • Use scientific notation. Write the factor as 1.66053906660e-27 in calculators or spreadsheets that accept e notation. For example, 12 amu becomes 12 * 1.66053906660e-27 kg.
  • Track units through the calculation. Multiplying amu by kg/amu cancels amu and leaves kg. This is a simple way to check that you used the right factor.
  • Choose precision deliberately. The conversion factor is exact by definition at the specified value, but an atomic or molecular mass you are converting may be rounded or represent an average. Your final answer should not imply more precision than the input supports.
  • Use a consistent convention. In chemistry, relative atomic masses may be average values reflecting naturally occurring isotopes, while a particular isotope has its own mass. Convert the specific value you actually need.
  • Convert back to verify when useful. Divide the kilogram result by 1.66053906660 × 10−27 kg/amu. The result should be close to your original amu value, allowing for rounding.

Troubleshooting

The result appears as 0. Your calculator may not display very small decimals. Use scientific notation or a calculator with exponent support; 1 amu is about 1.66e-27 kg, not zero.

The result is much too large. Check that you used the negative exponent and multiplied by the factor. Also confirm that the input was not already in kg or in a different unit such as grams.

The calculator rejects the input. The converter accepts nonnegative numerical values. Remove unit text, commas, or other characters and enter the number only. For a decimal, use the decimal point supported by your calculator.

Your hand calculation and converter differ slightly. Compare the number of significant figures and check whether you rounded the factor early. Recalculate with 1.66053906660 × 10−27, then round only the final answer.

You need a larger mass unit. Convert kilograms to grams by multiplying the kilogram result by 1,000. For instance, 1 amu is approximately 1.66053906660 × 10−24 g.

Frequently Asked Questions

What is the formula for converting amu to kg?
Multiply the amu value by 1.66053906660 × 10−27 kg/amu.

How many kilograms are in 1 amu?
One amu is approximately 1.66053906660 × 10−27 kg.

Are amu, u, and Da the same?
They are commonly used names or symbols for the same unit of mass in this conversion: the unified atomic mass unit, also called a dalton.

How do I convert 12 amu to kg?
Calculate 12 × 1.66053906660 × 10−27, giving approximately 1.99264687992 × 10−26 kg.

Why is the kilogram result so small?
The kilogram is a large unit compared with the mass of an atom. One atomic mass unit is only about 1.66 × 10−27 kilograms.

How do I convert kg back to amu?
Divide the kilogram value by 1.66053906660 × 10−27 kg/amu.

Related

Formula used
in amu | Mass | amu | 1 | 0
out kg | Mass | kg | amu * 1.66053906660e-27 | 6
out factor | Kilograms per amu | kg/amu | 1.66053906660e-27 | 11

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.

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