# Concentration unit converter

> Convert one concentration to every unit at once: M, mM, µM, mg/mL, µg/mL, % w/v, % w/w, ppm, ppb, molality, mole fraction, normality, with formulas.

URL: https://www.labcanvas.com/tools/concentration-converter

Enter one concentration in any unit, with the molar mass, and the converter shows it in every other unit at once: molarity (M, mM, µM, nM), mass concentration (g/L, mg/mL, µg/mL, ng/mL), % w/v, % w/w, ppm and ppb, molality, mole fraction and normality, each with its formula. For example, 150 mM NaCl (58.44 g/mol) is 8.766 g/L = 8.766 mg/mL = 0.8766 % w/v = 8766 ppm. Units based on the mass of solution or solvent (% w/w, molality, mole fraction) use the solution density, and ppm and ppb are taken as mg/L and µg/L for dilute aqueous solutions.

## Quick answer

- **What it does:** Converts a concentration from any unit to molarity, mass concentration, % w/v, % w/w, ppm/ppb, molality, mole fraction and normality at once.
- **Formula:** ρ (g/L) = c (mol/L) × M; % w/v = ρ/10; % w/w = ρ/(10d); ppm = ρ × 1000 (mg/L); molality b = 1000c/(1000d − cM); x = c/(c + (1000d − cM)/Mₛ); N = c × eq.
- **Example:** 37% w/w HCl (M = 36.46 g/mol, density 1.19 g/mL) is 440.3 g/L = 12.08 M, 16.11 mol/kg, mole fraction 0.2249.

Free, in the browser, no account needed. Updated 2026-10-19.

## Features

- Every unit at once from one input, with the formula used for each
- Molarity: M, mM, µM, nM; mass concentration: g/L, mg/mL, µg/mL, ng/mL
- % w/v and % w/w (with the solution density), ppm and ppb (mg/L and µg/L, dilute aqueous)
- Molality (mol/kg) and mole fraction, from the solution density and the solvent molar mass
- Normality with equivalents per mole (\(\ce{H2SO4}\) 2, \(\ce{H3PO4}\) 3, \(\ce{KMnO4}\) 5 in acid)
- Compound picker with molar masses from the CIAAW 2021 atomic weights, including common acids and bases
- Copy any value, the table, or download CSV

## How to use it

1. **Enter the concentration**: Type the value and pick its unit, for example 37 % w/w or 5 mg/mL.
2. **Give the solute**: Choose a compound or type its molar mass; for normality set the equivalents per mole.
3. **Check the density**: Leave 1.00 g/mL for dilute aqueous solutions, or enter the density for concentrated solutions; then read every unit from the table.

## At a glance

| | |
| --- | --- |
| Input | One concentration in any unit, the molar mass; density and equivalents where needed |
| Units | M, mM, µM, nM; g/L, mg/mL, µg/mL, ng/mL; % w/v; % w/w; ppm; ppb; mol/kg; mole fraction; N |
| Assumption | ppm = mg/L and ppb = µg/L (dilute aqueous); density 1.000 g/mL unless entered |
| Molar masses | CIAAW 2021 standard atomic weights |
| Output | Every unit at once with its formula; copy or CSV |

## How it works

Every unit is converted through the molar concentration \(c\) (mol/L) and the mass concentration \(\rho = c \times M\) (g/L), where \(M\) is the molar mass of the solute (g/mol). \(d\) is the density of the solution (g/mL, numerically kg/L), \(M_\mathrm{s}\) the molar mass of the solvent and \(\mathrm{eq}\) the equivalents per mole. One litre of solution weighs \(1000d\) g, of which \(\rho\) g is solute and \(1000d - \rho\) g solvent.

| Unit | From \(c\) and \(\rho\) | Back to \(c\) |
| --- | --- | --- |
| mg/mL, g/L | \(\rho = c \cdot M\) (1 mg/mL = 1 g/L) | \(c = \rho / M\) |
| % w/v (g/100 mL) | \(\rho / 10\) | \(c = 10 \cdot w / M\) |
| % w/w (g/100 g) | \(\rho / (10 \cdot d)\) | \(c = 10 \cdot w \cdot d / M\) |
| ppm, ppb (aqueous) | \(\rho \times 10^3\) mg/L, \(\rho \times 10^6\) µg/L | \(c = \mathrm{ppm} / (1000 \cdot M)\) |
| Molality \(b\) (mol/kg solvent) | \(1000c / (1000d - cM)\) | \(c = 1000 \cdot d \cdot b / (1000 + b \cdot M)\) |
| Mole fraction \(x\) | \(c / (c + (1000d - cM)/M_\mathrm{s})\) | \(c = 1000 \cdot d \cdot x / (x \cdot M + (1 - x) \cdot M_\mathrm{s})\) |
| Normality \(N\) (eq/L) | \(c \times \mathrm{eq}\) | \(c = N / \mathrm{eq}\) |

**Assumptions.** ppm and ppb are mass ratios; for water and dilute aqueous solutions 1 L weighs about 1 kg, so 1 ppm ≈ 1 mg/L and 1 ppb ≈ 1 µg/L, which is how they are used here. For concentrated solutions or other solvents use % w/w with the real density instead. % w/w, molality and mole fraction depend on the density; the default 1.000 g/mL is only right for dilute aqueous solutions. Molarity, mass concentration, % w/v and normality are per volume and change slightly with temperature; molality and mole fraction do not. IUPAC recommends amount concentration (mol/L) over normality, whose value depends on the reaction (\(\ce{H2SO4}\) is 2 eq/mol as an acid, \(\ce{KMnO4}\) 5 eq/mol as an oxidant in acid).

Sources: Cohen ER et al. *Quantities, Units and Symbols in Physical Chemistry* (IUPAC Green Book), 3rd ed. RSC Publishing; 2007, [doi:10.1039/9781847557889](https://doi.org/10.1039/9781847557889). Molar masses from Prohaska T et al. Standard atomic weights of the elements 2021. *Pure Appl Chem* 2022;94:573–600, [doi:10.1515/pac-2019-0603](https://doi.org/10.1515/pac-2019-0603).

## Worked examples: NaCl, concentrated HCl and H₂SO₄

**150 mM NaCl** (\(M = 58.44\ \mathrm{g/mol}\), density taken as 1.000 g/mL):

| Unit | Value | Working |
| --- | --- | --- |
| g/L = mg/mL | 8.766 | \(0.150 \times 58.44\) |
| µg/mL | 8766 | \(8.766 \times 1000\) |
| % w/v | 0.8766 | \(8.766 / 10\) |
| % w/w | 0.8766 | \(8.766 / (10 \times 1.000)\) |
| ppm (mg/L) | 8766 | \(8.766\ \mathrm{g/L} \times 1000\) |
| Molality | 0.1513 mol/kg | \(1000 \times 0.150 / (1000 - 8.766)\) |
| Mole fraction | 0.002719 | \(0.150 / (0.150 + 991.234 / 18.015)\) |
| Normality | 0.150 N | \(0.150 \times 1\) |

**Concentrated hydrochloric acid, 37% w/w** (\(M = 36.46\ \mathrm{g/mol}\)), with the density from the bottle, 1.19 g/mL: \(\rho = 10 \times 37 \times 1.19 = 440.3\ \mathrm{g/L}\), so \(c = 440.3 / 36.46 =\) **12.08 M**. Per litre there are \(1190 - 440.3 = 749.7\ \mathrm{g}\) of water, so the molality is \(1000 \times 12.08 / 749.7 = 16.11\ \mathrm{mol/kg}\) and the mole fraction of HCl 0.2249. To make 1 L of 1 M HCl, take \(1 / 12.08\ \mathrm{L} = 82.8\ \mathrm{mL}\) of the acid (\(C_1 V_1 = C_2 V_2\)), adding acid to water.

**Concentrated sulfuric acid, 96% w/w** (\(M = 98.07\ \mathrm{g/mol}\), density 1.84 g/mL): 1766.4 g/L, 18.01 M and, at 2 equivalents per mole, 36.02 N.

| From | To | Multiply by |
| --- | --- | --- |
| mg/mL | µg/mL | 1000 |
| mg/mL | % w/v | 0.1 |
| % w/v | g/L | 10 |
| mg/L (dilute aqueous) | ppm | 1 |
| µM | µg/mL | \(M / 1000\) |
| mg/mL | mM | \(1000 / M\) |

## Questions

### How do I convert mg/mL to molarity?

Divide by the molar mass: mg/mL equals g/L, so \(M = (\mathrm{mg/mL}) / (\mathrm{g/mol})\). For example, 5 mg/mL of glucose (180.16 g/mol) is \(5 / 180.16 = 0.02775\ \mathrm{M} = 27.75\ \mathrm{mM}\).

### How do I convert molarity to % w/v?

Multiply by the molar mass to get g/L, then divide by 10: \(\%\ \mathrm{w/v} = M \times \text{molar mass} / 10\). 150 mM NaCl is \(0.150 \times 58.44 / 10 = 0.8766\ \%\ \mathrm{w/v}\).

### How do I convert % w/w to molarity?

You need the density: \(M = 10 \times \%\ \mathrm{w/w}\) \(\times\, \text{density (g/mL)} / \text{molar mass}\). 37% HCl with density 1.19 g/mL is \(10 \times 37 \times 1.19 / 36.46 = 12.08\ \mathrm{M}\).

### Is ppm the same as mg/L?

For water and dilute aqueous solutions, yes: 1 L weighs about 1 kg, so \(1\ \mathrm{mg/L} \approx 1\ \mathrm{mg/kg} = 1\ \mathrm{ppm}\), and \(1\ \upmu\mathrm{g/L} \approx 1\ \mathrm{ppb}\). Strictly ppm is a mass ratio, so for dense or non-aqueous solutions use % w/w with the real density.

### What is the difference between molarity and molality?

Molarity is moles of solute per litre of solution; molality is moles per kilogram of solvent. They are close for dilute aqueous solutions (150 mM NaCl is 0.1513 mol/kg) but differ a lot for concentrated ones (37% HCl is 12.08 M but 16.11 mol/kg).

### How do I calculate normality?

Normality = molarity × equivalents per mole, where an equivalent is the amount that gives or takes one mole of \(\ce{H+}\) (acids and bases) or of electrons (redox). 1 M \(\ce{H2SO4}\) is 2 N; 0.02 M \(\ce{KMnO4}\) used as an oxidant in acid is 0.1 N.

### What is % w/v versus % w/w?

% w/v is grams of solute per 100 mL of solution; % w/w is grams per 100 g of solution. They are equal only when the density is 1 g/mL. Commercial concentrated acids are labelled in % w/w.