Percent Solution Calculator: % w/v, % w/w and % v/v Tool
Calculate the exact mass of solid solute or volume of liquid reagent required to prepare a percentage solution on an explicit weight-by-volume (% w/v), weight-by-weight (% w/w) or volume-by-volume (% v/v) basis. The interactive workspace loads a checked 5% w/v example in 200 mL and enforces strict basis separation.
Loads the independently checked preparation fixture case where a 5% w/v solution in 200 mL final volume requires 10 g of solute dissolved and brought up to 200 mL.
State the percentage basis explicitly in every protocol
Writing a bare percentage such as "10% SDS", "5% BSA" or "70% ethanol" in a methods section relies on laboratory convention unless the basis is stated alongside the number. Solid solutes dissolved in aqueous buffers, such as agarose, milk powder, BSA, SDS or trichloroacetic acid, are almost universally prepared as % w/v (grams per 100 mL of final volume). Miscible liquids such as ethanol, glycerol or Triton X-100 diluted into buffer are commonly prepared as % v/v, although viscous liquids like glycerol or PEG are often weighed gravimetrically as % w/w to avoid pipetting errors.
Because the three bases have different denominators, the workspace refuses ambiguous cross-basis requests (such as asking for a % w/w recipe with a millilitre final volume) rather than guessing a solution density of 1.0 g/mL.
Watch for non-additive volumes and commercial acid assays
Mixing miscible liquids such as ethanol and water causes slight volume contraction, so laboratory % v/v solutions are made by measuring the solute volume and bringing the mixture up to the final volume mark after mixing. When starting from a concentrated commercial reagent whose bottle label specifies an assay in % w/w (such as concentrated HCl, HNO3 or H2SO4), convert via the bottle density and molecular weight rather than treating the label percentage as % w/v.
Equations and variables
Weight-by-volume (% w/v) solute mass
msolute (g) = (P_wv / 100) × Vfinal (mL)
- msolute
- Mass of solid solute to weigh (g)
- P_wv
- Declared weight-by-volume percentage (grams of solute per 100 mL final solution)
- Vfinal
- Final solution volume after complete dissolution and make-up (mL)
Volume-by-volume (% v/v) and weight-by-weight (% w/w) relations
Vsolute (mL) = (P_vv / 100) × Vfinal (mL); msolute (g) = (P_ww / 100) × mfinal (g)
- Vsolute
- Volume of liquid solute measured before bringing to final volume Vfinal (mL)
- mfinal
- Total final mass of solute plus solvent for a gravimetric % w/w mixture (g)
- P_vv, P_ww
- Declared percentage on the stated volumetric or gravimetric basis
Scope and limitations
- No solution density or partial molar volume is assumed, so a % w/w specification cannot be converted into a final volume without an external density measurement.
- For % w/v and % v/v solutions, the denominator is the final total solution volume after mixing, not the volume of solvent added to the dry solid or neat liquid.
- Diluting a concentrated commercial acid or detergent supplied as % w/w (such as 37% w/w hydrochloric acid) requires its specific gravity or molarity rather than treating it as % v/v.
Sources and provenance
- Calculator inputs and independent arithmetic verificationOriginal synthetic inputs; see individual fixture notices
- Independent percent-solution verification casesPython fractions and decimal exact arithmetic reference
Technical questions
Why is 1% w/v defined as 1 gram per 100 mL of final solution?
In biological and pharmacopoeial laboratory practice, percent weight-by-volume (% w/v) is a conventional shorthand for grams of solute per 100 millilitres of final solution, matching the approximate density of dilute aqueous solutions at room temperature while keeping solid weighing and volumetric glassware aligned.
Why should I dissolve a solid in 80% of the water first instead of adding 200 mL of water to 10 g of powder?
Dissolving a solid solute occupies volume in the liquid phase. Adding 200 mL of water directly to 10 g of SDS, sucrose or BSA produces a final volume larger than 200 mL and under-concentrates the % w/v solution. Dissolve in a smaller volume first, then bring the meniscus to the final mark.
Can a % w/v concentration exceed 100%?
Yes, because the numerator (grams) and denominator (100 mL of final solution) have different physical dimensions, a dense or highly soluble salt can exceed 100 g per 100 mL of final solution. By contrast, % w/w and ideal % v/v fractions cannot exceed 100 percent.
Connected workflows
- DMSO stock reconstitution volume
Compare percentage recipes with molarity-based stock solution calculations.
- Serial dilution transfers and DMSO fractions
Plan downstream fold-dilution transfers from a prepared working stock.
- 4PL standard-curve interpolation
Use prepared blocking and wash solutions in immunoassay workflows.