Percent Solution Converter

Q: What units should density use?

g/mL. The equations assume densities in g·mL⁻¹.

Q: What if a target percent can’t be computed?

We show a note indicating which density is missing. Provide the required density to compute that conversion.

Convert between % w/w, % w/v, and % v/v. Provide solution density ρ (g·mL⁻¹) when converting mass↔volume, and solute density ρ_solute (g·mL⁻¹) when converting volume of solute ↔ mass of solute. See steps and visualize with a mini chart and a percent gauge.

Background

Definitions (per 100 units of solution):

% w/w = g solute per 100 g solution
% w/v = g solute per 100 mL solution
% v/v = mL solute per 100 mL solution

Bridging between these requires density: ρ = density of the solution (g·mL⁻¹), and ρ_solute = density of the solute (g·mL⁻¹).

w/v ↔ w/w: w/v = (w/w) × ρ and w/w = (w/v) ÷ ρ

v/v ↔ w/v: w/v = (v/v) × ρ_solute and v/v = (w/v) ÷ ρ_solute

w/w ↔ v/v: v/v = (w/w × ρ) ÷ ρ_solute and w/w = (v/v × ρ_solute) ÷ ρ

Enter known values

Convert from:

Percent must be between 0 and 100.

Densities (as needed):

For w/w↔w/v use ρ (solution). For v/v↔w/v use ρ_solute. For w/w↔v/v use both.

Show:

Step-by-step working

Mini chart: % w/w, % w/v, % v/v

Percent gauge

Round to sensible significant figures

Quick picks:

Chips prefill fields. Provide the densities shown (or your own) for complete conversions.

Result:

No results yet. Enter inputs and click Convert.

How to use this converter

Choose the source percent type and enter its value.
Provide ρ (solution) for w/w↔w/v; ρ_solute for v/v↔w/v; provide both for w/w↔v/v.
We compute all possible targets: % w/w, % w/v, % v/v. Missing densities will limit which outputs can be computed.

Formula & Equation Used

w/v ↔ w/w: w/v = (w/w) × ρ; w/w = (w/v) ÷ ρ

v/v ↔ w/v: w/v = (v/v) × ρ_solute; v/v = (w/v) ÷ ρ_solute

w/w ↔ v/v: v/v = (w/w × ρ) ÷ ρ_solute; w/w = (v/v × ρ_solute) ÷ ρ

Example Problems & Step-by-Step Solutions

Example 1 — 37% w/w HCl (ρ_solution=1.19 g/mL)

w/v = 37 × 1.19 = 44.03% w/v. (v/v needs ρ_solute, typically not used here.)

Example 2 — 5.00% w/v NaCl (ρ_solution=1.00 g/mL)

w/w = 5.00 ÷ 1.00 = 5.00% w/w. (v/v not applicable for solids without a meaningful ρ_solute.)

Example 3 — 70% v/v ethanol (ρ_solution=0.867 g/mL, ρ_solute=0.789 g/mL)

w/v = 70 × 0.789 = 55.23% w/v; w/w = 55.23 ÷ 0.867 ≈ 63.7% w/w.

Frequently Asked Questions

Q: When do I need densities?

Use ρ (solution) for w/w↔w/v; use ρ_solute for v/v↔w/v; use both for w/w↔v/v.

Q: What units should density use?

g/mL. The formulas above assume densities in g·mL⁻¹.

Q: What if a target percent can’t be computed?

We show a note indicating which density is missing. Add the required density to enable that conversion.

Solutions: Mass Percent