PPM Calculation Examples (10 Worked Problems) | Step-by-Step Solutions

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PPM Calculation Examples (10 Worked Problems) | Step-by-Step Solutions

Learning how to calculate parts per million (PPM) is an essential skill for anyone studying science, working in labs, or testing water, food, air, or soil quality. PPM allows us to describe very small concentrations in a way that’s easy to compare, understand, and communicate. In this guide, you’ll find 10 detailed, real-world PPM calculation examples—with step-by-step solutions to help you learn and practice with confidence.

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1. Calculating PPM of Salt in Water

Problem:
You dissolve 3 mg of salt in 1 liter of water. What is the PPM concentration?

Solution:
Use the formula:
PPM = (mg of solute) / (L of solution)

Plug in the numbers:
PPM = 3 mg / 1 L = 3 ppm

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2. Measuring Nitrate in Well Water

Problem:
A water sample from a well contains 10 mg of nitrate in 2 liters of water. What is the nitrate concentration in PPM?

Solution:
PPM = 10 mg / 2 L = 5 ppm

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3. Heavy Metals in Soil (mg/kg to PPM)

Problem:
A soil test finds 4 mg of lead in 1 kg of soil. What is the lead concentration in PPM?

Solution:
PPM = (mg of substance) / (kg of solid)
PPM = 4 mg / 1 kg = 4 ppm

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4. Carbon Monoxide in Air (Volume to PPM)

Problem:
Air contains 2 mL of carbon monoxide in 1,000,000 mL of air. What is the concentration in PPM?

Solution:
PPM = (Volume of gas / Total volume) × 1,000,000
PPM = (2 / 1,000,000) × 1,000,000 = 2 ppm

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5. Chlorine in Swimming Pool

Problem:
You add 15 mg of chlorine to 5 liters of pool water. What is the chlorine concentration in PPM?

Solution:
PPM = 15 mg / 5 L = 3 ppm

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6. Dye Concentration After Dilution

Problem:
You dissolve 20 mg of dye in 250 mL of water. What is the PPM?

Solution:
Convert 250 mL to liters: 250 mL = 0.25 L
PPM = 20 mg / 0.25 L = 80 ppm

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7. PPM to mg/L Conversion

Problem:
A water sample tests at 120 ppm calcium. How many mg/L is this?

Solution:
For water, 1 ppm = 1 mg/L
120 ppm = 120 mg/L

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8. Summing PPM for Mixed Solutes

Problem:
You dissolve 10 mg of sugar and 6 mg of salt in 2 liters of water. What is the total PPM of dissolved solids?

Solution:
Total dissolved = 10 mg + 6 mg = 16 mg
PPM = 16 mg / 2 L = 8 ppm

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9. PPM in Air by Mass

Problem:
A 10-liter air sample contains 0.005 grams of benzene vapor. What is the PPM by mass? (1 g = 1000 mg)

Solution:
Convert 0.005 g to mg: 0.005 g × 1000 = 5 mg
Assume air density ≈ 1 kg/m³ ⇒ 10 L = 0.01 m³ = 0.01 kg = 10,000 mg
PPM = (5 mg / 10,000 mg) × 1,000,000 = 500 ppm

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10. PPM in Food (mg/kg)

Problem:
A food sample contains 0.5 mg of iron per 100 g. What is the PPM?

Solution:
Convert 100 g to kg: 100 g = 0.1 kg
PPM = 0.5 mg / 0.1 kg = 5 ppm

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Tips for Accurate PPM Calculations

• Check your units: Always convert grams to milligrams, milliliters to liters, or grams to kilograms as needed.
• Use total final volume or mass: The denominator should always be the total solution or sample size.
• For water solutions: 1 mg/L is equal to 1 ppm—this makes quick calculations easy.
• For gases: Be sure to use the correct formula (by volume or mass).

If you need more help, explore the PPM Solution Calculator or MG/L to PPM Calculator.

For common errors, check out PPM Calculation Mistakes.