Molarity to Percent Calculator
Pick a solute (or enter a custom molar mass), type in a density, and convert freely between weight percent, molarity, and g/L.
Where M = 10 × d × wt% ÷ MW comes from
Start from definitions, not a shortcut. Weight percent (wt%) is the fraction of a solution's total mass that's dissolved solute — nothing about volume, nothing about moles. Molarity (M) is moles of solute per liter of solution volume. Density is the one number that bridges a mass fraction into a volume-based count, which is why it's the input this page can't avoid asking for.
Take exactly one liter of solution. Its mass is 1000 × d grams, with d in g/cm³ (numerically identical to g/mL). wt% of that mass is solute, so the solute mass in that liter is (wt% ÷ 100) × 1000 × d = 10 × d × wt% grams — worth keeping as its own quantity, because g/L is the number most dosing and inventory work actually wants. Divide by the solute's molar mass and grams become moles:
g/L = 10 × d × wt% = M × MW
wt% = M × MW ÷ (10 × d)
Nothing in that derivation assumes a particular solute — swap in any molar mass and the relationship still holds, which is the whole reason one calculator can stand in for eight different chemicals instead of needing eight separate ones. The one thing it genuinely cannot do is supply density for you. For six of the eight presets, this site's NaOH, KOH, HCl, H₂SO₄, HNO₃, and NH₃ calculators each interpolate density automatically from a cited reference table — use those directly rather than reading a density off a table and retyping it here. For NaCl and NaOCl, see the guidance table further down.
Two conditions have to hold for that arithmetic to be exact, and both are really about what "density" means in practice. First, d must be the solution's actual measured (or accurately tabulated) density at your concentration and temperature — not a value calculated by assuming volumes just add up. Most aqueous ionic solutions pack slightly denser than a linear blend predicts, and some pairs go much further: ethanol and water lose up to about 3.6% of their combined volume on mixing, as the alcohol + water volume contraction guide covers in detail, which is exactly why the dedicated ethanol–water dilution calculator uses a real measured curve instead of this page's simpler mass-balance formula. Second, wt% has to mean weight/weight — grams of solute per 100 g of solution. Swap in a weight/volume or volume/volume figure instead (see dilution math in practice for how those three diverge) and the 10× factor above no longer means what the derivation assumed.
Three ways people actually use this
Confirming a 25% NaOH tote against its COA
A receiving inspector wants to sanity-check a labeled 25% w/w caustic soda tote before it's logged into inventory, using the density already printed on the certificate of analysis.
- Solute
- NaOH
- Concentration
- 25.00% w/w
- Density
- 1.2739 g/cm³ (COA)
≈ 318.48 g/L, 7.96 mol/L — the same figure the dedicated NaOH calculator gives (see the validation note below).
Specifying a 3.00 M KOH electrolyte batch
An electrochemistry lab needs to order KOH liquor at a set molarity and has to tell the supplier what wt% assay to ship, using the density that supplier's own COA quotes.
- Solute
- KOH
- Molarity
- 3.00 mol/L
- Density
- 1.130 g/cm³ (COA)
≈ 14.90% w/w, 168.32 g/L — the number that goes on the purchase order.
Checking a dilute NaOCl working solution
A water-treatment operator diluted stock bleach down and wants to confirm it against a 12 g/L NaOCl target, using a density close to water's since the working solution is mostly water.
- Solute
- NaOCl
- Target
- 12.0 g/L
- Density
- 1.01 g/cm³ (dilute, ≈ water)
≈ 1.19% w/w, 0.16 mol/L — see the NaOCl labeling caveat under "where this goes wrong" below.
You still need a real density — here's where to get one
This calculator's accuracy is entirely bounded by the density you type in — the formula itself contributes no error, so the whole question is where that number comes from. Six of the eight presets already have a real answer built into this site: NaOH, KOH, HCl, H₂SO₄, HNO₃, and NH₃ each get a dedicated calculator that interpolates density from a cited, cross-checked reference table across their full practical range (NaOH tool, KOH tool, HCl tool, H₂SO₄ tool, HNO₃ tool, NH₃ tool) — use those directly instead of copying a number over by hand.
For the remaining two presets — NaCl and NaOCl — this site doesn't maintain an independently cross-checked density table, so treat the figures below as typical published anchor points — a starting estimate for a rough calculation, not a substitute for your own certificate of analysis when the result has to be accurate to better than a percent or two.
| Solute | Typical density | Note |
|---|---|---|
| NaCl (brine) | ≈1.20 g/cm³ at saturation (≈26.3% at 20°C) | Solubility, not this formula, sets the ceiling — you can't dose past ≈26.3% NaCl in water at room temperature. |
| NaOCl | ≈1.08 (household, ~6% available chlorine) to ≈1.21 (12.5% trade bleach) | "% available chlorine" on the label isn't the same figure as wt% NaOCl — see below before using this page for bleach dosing. |
Checking the math against numbers chemists already trust
Check 1 — against this site's own NaOH table. Run 25.00% NaOH at 1.2739 g/cm³ through this calculator and you get 7.96 mol/L — the same figure, to the same rounding, that comes out of the NaOH concentration calculator for the identical input, whose 1.2739 g/cm³ density is itself cross-checked against two independently published tables. The two tools run completely separate code (one interpolates a table, this one takes density as a raw input), so agreement here is a genuine check on the arithmetic, not a shared bug.
Check 2 — against the textbook "18 M sulfuric acid" figure. This site's H₂SO₄ calculator tables density out to 1.8305 g/cm³ at 100 wt% H₂SO₄. Run that through at MW 98.079 and you get 18.66 mol/L — close to, but not exactly, the "18 M" figure quoted constantly for concentrated sulfuric acid. The gap is real and instructive: that familiar 18 M number describes 98% w/w commercial-grade acid, not the pure 100% compound, and 98% acid is very slightly less dense than pure H₂SO₄. It's a useful reminder that "concentrated" is a grade, not an assay figure — the density you plug in has to match the actual wt%, not just the general strength of acid you're holding.
Where this goes wrong (it's never the arithmetic)
Every support question about a calculator like this one traces back to what went into it, not the formula itself:
- wt%, w/v%, and v/v% get typed into the same box. They're not interchangeable, and the gap between them scales with density — see dilution math in practice for how far off a mismatched basis can land you.
- Molar mass doesn't match the form actually being weighed. Order washing soda (Na₂CO₃·10H₂O, MW ≈ 286) but enter anhydrous sodium carbonate's molar mass (106) out of habit, and every output is off by nearly a factor of three.
- Molarity gets treated as normality. This page only outputs molarity. H₂SO₄ is 2 equivalents per mole as a diprotic acid, so 1 M H₂SO₄ is 2 N — mixing the two up in a titration calculation is one of the most common lab errors there is.
- Density and concentration are only paired at one temperature. A COA figure measured at 20°C applied to a solution sitting in a hot summer tank will be measurably wrong — aqueous density typically shifts on the order of a tenth of a percent per °C, small per degree but not small over a 15–20° swing.
- Density gets calculated instead of measured. Assuming pure-component volumes just add up is the single most common way to get a wrong density into this calculator — and it's wrong to varying degrees for almost every real mixture, most dramatically for ethanol and water (see the worked figures in the volume contraction guide and the dedicated ethanol–water dilution calculator).
- NaOCl's label percentage usually isn't wt% NaOCl. Commercial sodium hypochlorite is almost always sold by "% available chlorine" (a chlorine-equivalent figure), not literal mass-percent NaOCl — the two track together but aren't the same number. For bleach dosing work, skip the density step entirely and use the bleach dilution calculator, which works in available-chlorine percent directly.
- Solid solutes get pushed past their solubility limit. Nothing stops you from typing 40% NaCl into the wt% field, but no such solution exists at room temperature — NaCl tops out around 26.3% in water at 20°C. The formula will still return a number; it just won't describe anything real.
Once you have a trustworthy molarity or wt% figure out of this page, diluting it down to a working strength is a separate calculation — the solution dilution calculator handles a single C₁V₁ = C₂V₂ step, and the serial dilution calculator handles a whole dilution series at once.
Frequently asked questions
Why does this calculator make me type in a density, when the NaOH tool on this site finds it automatically?
Because there's no single density curve that covers eight unrelated chemicals. NaOH, KOH, HCl, H2SO4, HNO3, and NH3 each got their own dedicated calculator specifically because their density-versus-concentration relationship needed a real, individually sourced reference table — that's six separate tables already, and NaCl and NaOCl don't have a site-verified one at all. Instead of forcing all eight through one converter that tried to carry six-plus full tables, this page asks for the one number that makes the underlying math solute-agnostic — density — so it works the same way whether that number comes from one of this site's own dedicated tools or from your own certificate of analysis.
Where do I actually find a density I can trust, for NaCl or NaOCl — the two presets without a dedicated calculator?
In order of reliability: your own supplier's certificate of analysis for that specific lot — production density varies batch to batch more than most people expect; a standard chemical-engineering reference like the CRC Handbook of Chemistry and Physics or Perry's Chemical Engineers' Handbook; or a direct hydrometer reading if you have the material in hand. The guidance table above gives typical anchor points for those two presets, but "typical" is exactly that — a starting estimate, not a substitute for a real COA once the number has to hold up on paper. The other six presets don't need any of that: pick NaOH, KOH, HCl, H2SO4, HNO3, or NH3 from the dropdown and this site's own dedicated calculator for that solute hands you a cited density directly.
What's the difference between molarity and normality, and which one does this page give me?
This calculator only ever outputs molarity — moles of solute per liter. Normality (equivalents per liter) equals molarity times the number of reactive equivalents per mole, and that multiplier depends on the reaction, not just the compound: H2SO4 is 2 N per M when it's donating two protons as an acid, but a different factor entirely in a redox context. Because normality is reaction-dependent rather than solute-dependent, this page deliberately doesn't try to guess it — multiply the molarity result by your own reaction's equivalence factor.
The solute I'm using isn't in the dropdown — can I still use this calculator?
Yes — pick "Custom solute…" and type its molar mass directly into the field that unlocks. Molar mass is just the sum of atomic weights in the formula, which you can pull from the compound’s safety data sheet, its PubChem entry, or by adding up a periodic table by hand; once it’s in the field, the calculator treats it exactly like any built-in preset.
I estimated my density by assuming volumes just add up, and the result looks off — why?
Because that assumption is usually wrong. Real solutions rarely occupy the same volume as their pure components combined — ionic solutes tend to pack a mixture slightly denser than a linear blend predicts, and some pairs, most famously ethanol and water, lose noticeably more volume than that on mixing. Either way, a density calculated from "ideal" mixing can be off by a percent or more, and because density sits directly inside this formula, that error carries straight through to your molarity or wt% result. Use a measured or tabulated density here, never a calculated one, whenever the answer needs to be trustworthy.
How accurate is the result, assuming I trust my density and molar mass inputs?
As accurate as those two inputs — full stop. Unlike the NaOH, HCl, and H2SO4 calculators, there’s no curve-fitting or interpolation happening here to add its own small error on top. M = 10 × d × wt% ÷ MW is an exact mass-balance identity, not a fitted approximation, so if density and molar mass are both correct for your actual solution, the arithmetic itself contributes zero additional error.