All calculatorsPercent Solution Converter
Convert between % w/w, % w/v, and % v/v. Provide solution density ρ (g·mL⁻¹) when converting mass↔volume, and solute density ρsolute (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 ρsolute = 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) × ρsolute and v/v = (w/v) ÷ ρsolute
w/w ↔ v/v: v/v = (w/w × ρ) ÷ ρsolute and w/w = (v/v × ρsolute) ÷ ρ
How to use this converter
- Choose the source percent type and enter its value.
- Provide ρ (solution) for w/w↔w/v; ρsolute 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) × ρsolute; v/v = (w/v) ÷ ρsolute
w/w ↔ v/v: v/v = (w/w × ρ) ÷ ρsolute; w/w = (v/v × ρsolute) ÷ 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 ρsolute, 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 ρsolute.)
Example 3 — 70% v/v ethanol (ρ_solution=0.867 g/mL, ρsolute=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 ρsolute 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.
