Molarity in mol/L is calculated from density by the formula M = (density in g/mL × mass fraction × 1000) ÷ molar mass in g/mol, so any density-to-molarity conversion is really two separate jobs: get the density into g/mL (or convert it from g/cm³, kg/m³, lb/ft³, lb/gal and other units), and then plug it into the chemistry formula together with the solute's mass percent and molar mass. The density value is the unit-conversion half of the problem — that part is mechanical — while the rest of the job is pure chemistry that no calculator can replace. The most common snag is that density values in real life are almost never already in g/mL: spec sheets use g/cm³, scientific papers use kg/m³, and North American industry uses lb/ft³ or lb/gal. That mismatch between units is exactly why a dedicated density unit converter belongs in this workflow, and the conversion factors used below come straight from the same SI definitions the converter is built on.
Once the density is in g/mL and you have the mass percent of the solute and its molar mass, the rest is a single multiplication and division. Everything in this article is laid out so you can do the chemistry by hand, with the unit-conversion step handled in seconds and without leaving the page.
The Density-to-Molarity Formula
For a solution whose composition is given as a mass percent, the relationship between density, mass percent, and molarity is:
M (mol/L) = ρ (g/mL) × w × 1000 ÷ Mm (g/mol)
where ρ is the density of the solution in grams per milliliter, w is the mass fraction of the solute (so a 10 % solution has w = 0.10), and Mm is the molar mass of the solute in grams per mole. The factor 1000 converts the 1000 mL in a liter into the right scale: density (g/mL) × 1000 mL/L gives the mass of one liter in grams, multiplying by w gives the grams of solute in that liter, and dividing by Mm turns those grams into moles per liter. The result, by definition, is moles of solute per liter of solution — exactly what molarity measures.
If you only know volume percent or mole percent, the formula is different and you cannot simply substitute it for w — use the version that matches the concentration unit on the label or in the reference table. If you do not know the composition of the solution at all, density alone is not enough information, and no formula will recover molarity from it.
How to Convert Density to Molarity
- Find the solution's mass percent (w). Read it from the bottle label, the safety data sheet, the problem statement, or a reference table. Without w, the formula has no input — stop here and look up the composition before going further.
- Find the solute's molar mass (Mm). Look it up from the chemical composition. Sodium chloride (NaCl) is 58.44 g/mol, glucose (C6H12O6) is 180.16 g/mol, sucrose (C12H22O11) is 342.30 g/mol. For hydrated salts, use the molar mass of the hydrated form — anhydrous and decahydrate give different answers.
- Convert the density to g/mL. If your density is already in g/mL or g/cm³, you are done — they are identical. If it is in kg/m³, divide by 1000. If it is in lb/ft³, multiply by 0.016018463. If it is in lb/gal (US), multiply by 0.11982643. For any other unit, use the density converter to step between g/cm³, kg/m³, lb/ft³, g/L, kg/L, mg/mL, lb/in³, oz/in³, lb/gal, and back, instantly and in your browser.
- Plug into M = ρ × w × 1000 ÷ Mm. Multiply the three numbers together, divide by the molar mass, and report the result in mol/L (which is the same as M or molar). Keep one or two extra significant figures during the calculation and round only at the end.
- Sanity-check against the water anchor. Pure water at 4 °C is 1 g/mL, so an aqueous solution's density should land somewhere near that value — far above it usually indicates a heavy dissolved salt, far below it usually indicates a light organic solvent. If your value is wildly off the anchor, the units step almost certainly has a factor error.
Get the Density into g/mL First
The chemistry formula only accepts g/mL, but density values arrive in many different units. The exact factors you need are:
| If your density is in | Operation | Equivalent statement |
|---|---|---|
| g/cm³ | identity | 1 g/cm³ = 1 g/mL |
| kg/m³ | divide by 1000 | 1000 kg/m³ = 1 g/mL |
| g/L | divide by 1000 | 1000 g/L = 1 g/mL |
| kg/L | identity | 1 kg/L = 1 g/mL |
| mg/mL | divide by 1000 | 1000 mg/mL = 1 g/mL |
| lb/ft³ | multiply by 0.016018463 | 1 lb/ft³ = 0.016018463 g/mL |
| lb/gal (US) | multiply by 0.11982643 | 1 lb/gal = 0.11982643 g/mL |
| lb/in³ | multiply by 27.679905 | 1 lb/in³ = 27.679905 g/mL |
These are not rounded approximations — they come from the exact definitions of the pound (0.45359237 kg), the inch (0.0254 m), the foot (0.3048 m), and the US gallon (231 in³), matching the NIST SP 811 guide for the International System of Units. Because the chemistry formula treats density as a multiplicative factor, even small unit errors propagate straight into the final molarity, so it pays to use the exact factors rather than memorizing rough rules of thumb.
The fastest path is to type the value once into the density converter, set "From" to whatever unit your source uses, set "To" to g/mL, and read the answer. For values that mix conventions — say, a spec sheet in lb/gal alongside a paper in kg/m³ — ticking the "show all units at once" option gives every supported unit in a single table, so the g/mL column lands next to the original value for a one-glance cross-check. If you want a deeper walk-through of just the unit-conversion step, the guide on how to convert density between units covers every supported pair.
Worked Example: 10 % Sodium Chloride Solution
Take an aqueous sodium chloride solution labeled "10 % w/w" at 20 °C. From a reference table, its density is 1.07 g/cm³ (which equals 1.07 g/mL with no conversion needed), and the molar mass of NaCl is 58.44 g/mol.
Step 1. Density in g/mL: ρ = 1.07 g/mL (already correct).
Step 2. Mass fraction: w = 10 % = 0.10.
Step 3. Molar mass: Mm = 58.44 g/mol.
Step 4. Apply the formula:
M = ρ × w × 1000 ÷ Mm M = 1.07 × 0.10 × 1000 ÷ 58.44 M = 107 ÷ 58.44 M = 1.831 mol/L
So a 10 % w/w sodium chloride solution is roughly 1.83 M. If the density had been quoted in kg/m³ (1070 kg/m³) instead of g/mL, you would divide by 1000 first to get 1.07 g/mL, and the rest of the calculation is unchanged. If it had been quoted in lb/gal (about 8.93 lb/gal), multiplying by 0.11982643 gives the same 1.07 g/mL — which is exactly the unit step the density converter handles in one keystroke.
Why Density Alone Is Never Enough
Density is mass per volume. Molarity is moles of solute per volume of solution. The link between them is the composition — how much of the mass is the solute you actually care about — together with the solute's molar mass to turn grams into moles. A 1.0 g/mL solution of pure water has zero molarity of any solute, and a 1.0 g/mL solution of 5 % glucose has a completely different molarity from a 1.0 g/mL solution of 5 % sucrose, even though the densities match. Two values of density that look identical can hide order-of-magnitude differences in molarity, which is why the chemistry inputs always matter more than the density conversion itself.
Practical cases where the formula still applies but you need an extra step include hydrated salts (use the molar mass of the hydrated form, not the anhydrous), mixtures with multiple solutes (compute each solute's molarity from its own w and Mm), and non-ideal solutions at high concentration (real densities deviate slightly from the textbook values, so a measured density is always more trustworthy than a tabulated one). For temperature-sensitive work, always pair the density with its measurement temperature — a "1.07 g/mL" at 20 °C is not the same number at 40 °C.
Common Density Anchors Worth Memorising
A handful of density values come up often enough to act as anchor points when you eyeball a converted number:
| Substance | g/cm³ | kg/m³ | lb/ft³ |
|---|---|---|---|
| Pure water (4 °C) | 1.000 | 1000 | 62.428 |
| Seawater (typical) | 1.025 | 1025 | 64.0 |
| Ethanol (20 °C) | 0.789 | 789 | 49.3 |
| Glycerol | 1.261 | 1261 | 78.7 |
| Aluminum | 2.70 | 2700 | 168.6 |
| Steel | 7.85 | 7850 | 490 |
| Mercury | 13.534 | 13534 | 845 |
If you ever convert something that should be aqueous and end up with a density of 1.07 g/mL, 1.20 g/mL, or similar, the most likely explanation is a percentage or two of dissolved solute — values far outside that range usually mean either an organic solvent (below 1 g/mL) or a concentrated brine or acid (well above 1 g/mL). The full set of supported units, including g/cm³, kg/m³, lb/ft³, g/mL, kg/L, mg/mL, lb/in³, oz/in³, lb/gal, and g/L, is converted client-side in the browser so nothing about your sample leaves the device.