All calculatorsPPM to Molarity Calculator
Convert solution concentration between ppm and molarity M (mol·L⁻¹). Assumes 1 ppm ≈ 1 mg/L in dilute aqueous solutions by default, with an option to specify solution density ρ for more general cases.
Background
In dilute water, 1 ppm ≈ 1 mg/L. Then M = (ppm / 1000) / Mᵣ, where Mᵣ is molar mass (g·mol⁻¹). For non-aqueous or concentrated solutions, include the solution density ρ (kg·L⁻¹): mg/L = ppm × ρ.
How to use this calculator
- Choose the direction: ppm → M or M → ppm.
- Enter the solute’s molar mass Mᵣ (g·mol⁻¹).
- Provide ppm or M according to the direction.
- Select density: assume water (ρ=1) or input a custom ρ (kg·L⁻¹).
- Click Calculate or use Quick picks (auto-calculates).
Formula & Equation Used
Water (dilute): 1 ppm ≈ 1 mg·L⁻¹
General: mg·L⁻¹ = ppm × ρ (kg·L⁻¹)
ppm → M: M = (ppm × ρ / 1000) / Mᵣ
M → ppm: ppm = (1000 × M × Mᵣ) / ρ
Example Problems & Step-by-Step Solutions
Example 1 — 100 ppm NaCl → M (water)
ppm → mg·L⁻¹: 100 ppm ≈ 100 mg·L⁻¹.
M = (100/1000) / 58.44 = 0.1 / 58.44 ≈ 1.71×10⁻³ mol·L⁻¹.
Example 2 — 0.010 M H₂SO₄ → ppm (water)
ppm = 1000 × 0.010 × 98.079 ≈ 981 ppm.
Frequently Asked Questions
Q: When is 1 ppm = 1 mg/L valid?
For dilute aqueous solutions near ρ ≈ 1 kg·L⁻¹. Otherwise use custom ρ.
Q: Units for density?
kg·L⁻¹ (same as g·mL⁻¹). Water at 25 °C ≈ 0.997 kg·L⁻¹ (≈1.00).
Q: What if my solution is concentrated?
Use a measured or literature density instead of assuming ρ = 1.
