How to Calculate % Purity: Formula & Worked Example

This calculator works out the percentage purity of a substance from the mass of the pure substance and the mass of the crude sample. You enter the measured pure mass and the total sample mass, and you get the purity as a percentage, which tells you how much of your sample is actually the desired compound.

Formula

Purity (%) = (mass of pure substance / mass of crude sample) × 100

Where:

• Mass of pure substance (g) – the amount of the desired compound in the sample, measured after purification or determined by an analytical method.
• Mass of crude sample (g) – the total mass of the material you started with, including impurities.
• Purity (%) – the percentage of the sample that is the desired substance.

This formula assumes both masses are in the same unit (grams, kilograms, etc.). The result is a dimensionless percentage.

Worked Example

Using the calculator defaults: pure mass = 4.8 g, total sample mass = 5.0 g.

1. Write the formula: Purity = (pure mass / total mass) × 100
2. Plug in the numbers: Purity = (4.8 / 5.0) × 100
3. Divide: 4.8 ÷ 5.0 = 0.96
4. Multiply by 100: 0.96 × 100 = 96%

The purity is 96%. This matches the calculator output.

When to Use This Calculation

Percentage purity is used in chemistry labs, pharmaceuticals, and manufacturing to assess the quality of a product. It is relevant when you have a crude mixture and need to know how much of it is the active ingredient. For example, a drug tablet may contain the active compound plus binders and fillers; the purity tells you the fraction of active ingredient. It is also used in stoichiometry to adjust reaction quantities when reagents are not 100% pure.

How to Read the Result

A purity of 100% means the sample is entirely the desired substance with no impurities. A value below 100% indicates the presence of other materials. For many applications, a purity above 98% is considered high, but the acceptable threshold depends on the context (e.g., analytical standards often require >99.9%).

Common Mistakes

• Using different units – mixing grams and milligrams without conversion gives a wrong ratio. Always convert to the same unit first.
• Reversing the numerator and denominator – purity is always (pure / total) × 100, not (total / pure). Reversing gives a number over 100% that is meaningless.
• Forgetting to multiply by 100 – the raw ratio (e.g., 0.96) is not a percentage. You must multiply by 100.
• Rounding too early – rounding intermediate values can change the final percentage. Keep extra digits until the end.
• Confusing purity with yield – yield is the amount of product obtained compared to theoretical maximum; purity is the fraction of that product that is the desired compound. They are different.

Tips

• Always measure both masses on the same balance and at the same time to avoid drift.
• If the pure mass comes from a titration or spectroscopy, make sure you convert the analytical result to a mass correctly.
• For solids, dry the sample before weighing to remove moisture, which would otherwise count as impurity.
• Use the calculator to double-check your hand calculations, but understand the formula so you can catch errors.
• When reporting purity, include the method used (e.g., “by HPLC”) because different methods can give slightly different values.

Troubleshooting

Result is over 100% – This usually means the pure mass is larger than the total mass, which is impossible. Check your inputs: did you enter the correct values? Did you accidentally swap them? Also, if your sample absorbed moisture, the pure mass might appear higher than it should.

Result is negative – Negative masses are not physically possible. Ensure both inputs are positive numbers. If you entered a negative number, correct it.

Result is very low (e.g., 5%) – This could be correct if the sample is heavily diluted, but double-check that your pure mass is actually the mass of the desired substance, not the mass of a derivative or complex.

Calculator shows an error – If the total mass is zero, the division fails. Enter a positive total mass.

Units mismatch – If you enter pure mass in grams and total mass in kilograms, the calculator will treat them as the same unit. Convert manually to match.

Frequently Asked Questions

Q: Can purity be more than 100%?
A: No, by definition purity is the fraction of the desired substance in the sample, so it cannot exceed 100%. A result above 100% indicates an error in measurement or calculation.

Q: What is the difference between purity and assay?
A: They are often used interchangeably, but “assay” can also refer to the quantitative determination of a substance’s concentration. Purity specifically refers to the fraction of the desired compound in a sample.

Q: How do I find the mass of pure substance?
A: It depends on the method. For a purified solid, you can weigh it directly. For a mixture, you might use chromatography, titration, or spectroscopy to determine the amount of the target compound, then convert that to a mass.

Q: Does purity affect chemical reactions?
A: Yes. If a reagent is not pure, the actual amount of reactive substance is lower than the weighed mass. You may need to adjust the quantity used to get the correct stoichiometric amount.

Q: Can I use this formula for liquids or gases?
A: Yes, as long as you have the mass of the pure substance and the total mass of the sample. For liquids, you might need to measure density and volume to get mass.

Q: What is a good purity percentage?
A: It depends on the application. For analytical standards, >99.9% is typical. For industrial chemicals, 95-98% is often acceptable. For food or drugs, regulatory limits apply, but this calculator does not provide those.

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in pure | Mass of pure substance | g | 4.8 | 0
in total | Mass of crude sample | g | 5.0 | 0
out purity | Purity | % | (pure / total) * 100 | 2