Percentage Concentration to Molarity Calculator
How it Works
01Pick a Solution Preset
13 common reagents pre-loaded (HCl, H₂SO₄, NH₃, NaOH, etc.) or pick custom and enter any MW.
02Enter Density and Percentage
Density in g/cm³ (= g/mL) from supplier datasheet; mass percent w/w from the bottle label.
03Apply M = % × ρ × 10 / MW
Standard conversion: 37% HCl × 1.19 g/cm³ × 10 / 36.46 g/mol = 12.07 M.
04Get Molarity + Mass Conc.
Output in M / mM / µM, plus mass concentration in g/L = mg/mL for cross-checking.
What is a Percentage Concentration to Molarity Calculator?
The calculator includes 13 common reagent presets with auto-filled molar masses, eliminating the most common error source (using the wrong MW): Ammonia 17.03, Acetic acid 60.05, Ethanol 46.07, Formaldehyde 30.03, Glucose 180.16, Hydrochloric acid 36.46, Hydrogen peroxide 34.01, Nitric acid 63.01, Phosphoric acid 98.00, Potassium hydroxide 56.11, Sodium chloride 58.44, Sodium hydroxide 40.00, and Sulfuric acid 98.08 g/mol. For any compound not in the list, "Set custom molar mass" mode lets you enter the MW directly. Density input accepts g/cm³, g/mL, kg/L, or kg/m³.
Output: molarity in M / mM / µM simultaneously plus the equivalent mass concentration in g/L (= mg/mL) for cross-checking. The result panel shows the full transparent calculation breakdown: input quantities → mass concentration → moles → molarity. Smart warnings catch unphysical values (MW < 1 g/mol or > 1 MDa, density < 0.5 or > 5 g/cm³) and unrealistic concentrations beyond saturation limits (M > 30 mol/L). Designed for analytical chemists preparing working solutions from concentrated stocks, biochemists making buffer dilutions, organic chemists scaling up reactions from supplier specs, students learning stoichiometric conversions, and anyone needing a fast bottle-label-to-molarity conversion — runs entirely in your browser, no account, no data stored.
Pro Tip: Pair this with our Molarity Calculator for forward calculations, our Dilution Factor Calculator for serial dilution, our Molality Calculator for colligative-property work, or our Mass Percent Calculator for the reverse conversion.
How to Use the Percentage Concentration to Molarity Calculator?
How is percentage to molarity calculated?
Converting % w/w to molarity is the first step in working with any concentrated commercial reagent. The math is straightforward; getting the density right at your exact concentration is the most common source of error.
References: CRC Handbook of Chemistry and Physics; supplier (Sigma-Aldrich, Fisher, VWR) reagent datasheets; IUPAC Compendium of Chemical Terminology.
Core Formula
M (mol/L) = (% × ρ × 10) / MW
Where % is mass percent (w/w), ρ is solution density in g/cm³ (= g/mL), and MW is molar mass in g/mol. The factor 10 comes from converting (1 g/cm³ → 1000 g/L) × (1/100 from %) = 10.
Algebraic Derivation
- Consider 1 L = 1000 mL of solution.
- Mass of solution = ρ × 1000 mL = 1000ρ grams.
- Mass of solute = (%/100) × 1000ρ = 10·%·ρ grams.
- Moles of solute = mass / MW = (10·%·ρ) / MW.
- Molarity = moles per liter = (10·%·ρ) / MW mol/L.
Worked Example — Concentrated HCl
Bottle label: 37% w/w HCl, density 1.19 g/cm³. MW(HCl) = 36.46 g/mol.
- M = (37 × 1.19 × 10) / 36.46 = 440.3 / 36.46 = 12.07 mol/L = 12.07 M.
- Mass concentration = 37 × 1.19 × 10 = 440.3 g/L.
- This is the canonical "12 M HCl" used as the lab concentrated stock.
Worked Example — Concentrated H₂SO₄
Bottle label: 98% w/w H₂SO₄, density 1.84 g/cm³. MW(H₂SO₄) = 98.08 g/mol.
- M = (98 × 1.84 × 10) / 98.08 = 1803.2 / 98.08 = 18.38 mol/L = 18.38 M.
- Mass concentration = 1803.2 g/L.
- This is the canonical "18 M H₂SO₄" used as the lab concentrated stock; produces enormous heat on dilution — always add acid TO water.
Worked Example — Aqueous Ammonia
Bottle label: 28% w/w NH₃ (aqueous ammonia), density 0.90 g/cm³. MW(NH₃) = 17.03 g/mol.
- M = (28 × 0.90 × 10) / 17.03 = 252 / 17.03 = 14.80 mol/L = 14.80 M.
- Often labeled "concentrated ammonia" or "ammonium hydroxide"; is volatile and loses ammonia over time when not properly sealed (concentration drops with bottle age).
Common Concentrated Reagents (Reference Values)
- HCl, 37% w/w, ρ 1.19: 12.07 M.
- HBr, 48% w/w, ρ 1.49: 8.84 M.
- HI, 57% w/w, ρ 1.70: 7.57 M.
- HNO₃, 70% w/w, ρ 1.42: 15.78 M.
- HNO₃, fuming 90% w/w, ρ 1.50: 21.4 M.
- H₂SO₄, 98% w/w, ρ 1.84: 18.38 M.
- HClO₄, 70% w/w, ρ 1.66: 11.54 M.
- H₃PO₄, 85% w/w, ρ 1.69: 14.66 M.
- Glacial acetic acid, 99.7% w/w, ρ 1.05: 17.42 M.
- Formic acid, 88% w/w, ρ 1.20: 22.94 M.
- NaOH, 50% w/w, ρ 1.52: 19.00 M.
- KOH, 45% w/w, ρ 1.46: 11.71 M.
- NH₃ aq, 28% w/w, ρ 0.90: 14.80 M.
- H₂O₂, 30% w/w, ρ 1.11: 9.79 M.
- H₂O₂, 50% w/w, ρ 1.20: 17.65 M.
The Inverse Conversion (Molarity → %)
% w/w = (M × MW) / (10 × ρ)
Useful when you have a target molarity and want to know what mass-percent bottle to order. Example: 1.0 M aqueous NaOH, ρ ≈ 1.04 → % = (1.0 × 40) / (10 × 1.04) = 3.85% w/w.
Worked Example — Make 1 L of 1 M NaOH from 50% Stock
Question: The lab has a stock bottle labeled "50% w/w NaOH (sodium hydroxide), density 1.52 g/cm³." How do I make 1 L of 1.0 M NaOH from this stock?
Step 1 — Compute the Stock Molarity.
- MW(NaOH) = 40.00 g/mol.
- M_stock = (50 × 1.52 × 10) / 40.00 = 760 / 40.00 = 19.0 M NaOH.
Step 2 — Compute the Dilution. Use C₁V₁ = C₂V₂.
- C₁ = 19.0 M (stock); C₂ = 1.0 M (target); V₂ = 1000 mL (target volume).
- V₁ = (C₂ × V₂) / C₁ = (1.0 × 1000) / 19.0 = 52.6 mL of 50% NaOH stock.
Step 3 — Procedure.
- To a 1 L volumetric flask, add about 700 mL of distilled water.
- Slowly add 52.6 mL of 50% NaOH stock (use a calibrated graduated cylinder; concentrated NaOH is highly caustic — wear PPE).
- Swirl gently; the dissolution is exothermic so let cool to room T before final adjustment.
- Top up to 1.000 L mark with distilled water; stopper and invert 10-20 times to mix.
- Label: "1.0 M NaOH, [date], [initials]."
Step 4 — Verify.
- Predicted moles in final solution: 52.6 mL × 19.0 M / 1000 = 1.000 mol.
- In 1 L: 1.000 mol/L = 1.0 M ✓.
- For high-precision titration use, standardize the prepared solution against potassium hydrogen phthalate (KHP) — atmospheric CO₂ absorption can reduce effective NaOH concentration over time.
Step 5 — Safety.
- 50% NaOH is extremely caustic — causes severe skin burns and eye damage on contact.
- Always add NaOH to water (never water to concentrated NaOH; the heat-of-dilution can cause violent splashing of caustic solution).
- PPE: lab coat, full face shield, neoprene/nitrile gloves, closed-toe shoes.
- Spill response: dilute with copious water; do NOT use acid to neutralize a NaOH spill (exothermic, splashing hazard).
Who Should Use the % → Molarity Calculator?
Technical Reference
The Conversion Formula and Its Derivation. The relationship M = (% × ρ × 10) / MW arises from dimensional analysis. Consider 1 L of solution: total mass = ρ × 1000 mL = 1000·ρ grams (where ρ is density in g/cm³). The mass of solute = (%/100) × 1000·ρ = 10·%·ρ grams. Moles of solute = (10·%·ρ) / MW (where MW is in g/mol). Molarity = moles per liter = (10·%·ρ) / MW. The 10 factor combines the 1000 (g/cm³ × mL → g/L) and 1/100 (% → fraction) factors: 1000/100 = 10.
Density Dependence on Concentration. For aqueous solutions, density rises with solute concentration in a smooth but non-linear way. HCl: 10% w/w 1.048 g/cm³; 20% 1.098; 30% 1.149; 37% 1.190. H₂SO₄: 10% 1.066; 30% 1.219; 50% 1.395; 70% 1.610; 90% 1.814; 98% 1.840 (max ~1.842 at 99%). NaOH: 10% 1.109; 25% 1.274; 50% 1.524. HNO₃: 10% 1.054; 30% 1.180; 50% 1.310; 70% 1.413; 90% 1.483. Always use the density at YOUR exact concentration — using a generic value introduces 5-15% error.
Temperature Dependence. Density decreases with increasing temperature (~0.05% per °C for typical aqueous reagents). Molarity also drifts slightly with T because volume changes (~0.5% drop per 10 °C rise). For routine work at controlled lab T (20-25 °C), the correction is negligible; for high-precision NIST-traceable work, specify and control T to ±0.1 °C and use density tables at the exact T.
Common Concentrated Lab Reagents (Reference Table).
- Hydrochloric acid (HCl): 37% w/w, ρ 1.190 g/cm³, MW 36.461 → 12.07 M.
- Hydrobromic acid (HBr): 48% w/w, ρ 1.490 g/cm³, MW 80.911 → 8.84 M.
- Hydroiodic acid (HI): 57% w/w, ρ 1.70 g/cm³, MW 127.91 → 7.57 M.
- Nitric acid (HNO₃): 70% w/w, ρ 1.413 g/cm³, MW 63.013 → 15.69 M; fuming 90% ρ 1.503 → 21.46 M.
- Sulfuric acid (H₂SO₄): 98% w/w, ρ 1.840 g/cm³, MW 98.079 → 18.38 M; oleum (fuming) ρ 1.94+ depending on % SO₃.
- Perchloric acid (HClO₄): 70% w/w, ρ 1.660 g/cm³, MW 100.46 → 11.56 M.
- Phosphoric acid (H₃PO₄): 85% w/w, ρ 1.685 g/cm³, MW 97.995 → 14.62 M.
- Glacial acetic acid (CH₃COOH): 99.7% w/w, ρ 1.049 g/cm³, MW 60.052 → 17.42 M.
- Formic acid (HCOOH): 88% w/w, ρ 1.197 g/cm³, MW 46.025 → 22.89 M; 99% ρ 1.221 → 26.27 M.
- Sodium hydroxide (NaOH): 50% w/w, ρ 1.524 g/cm³, MW 39.997 → 19.05 M.
- Potassium hydroxide (KOH): 45% w/w, ρ 1.460 g/cm³, MW 56.106 → 11.72 M.
- Ammonia aqueous (NH₃ aq, "ammonium hydroxide"): 28-30% w/w as NH₃, ρ 0.898-0.910 g/cm³, MW 17.031 → 14.78-16.04 M.
- Hydrogen peroxide (H₂O₂): 30% w/w, ρ 1.111 g/cm³, MW 34.015 → 9.80 M; 50% ρ 1.196 → 17.59 M; 70% ρ 1.290 → 26.55 M (rocket-grade).
Hydrate vs Anhydrous Reagents. Many crystalline salts come as hydrates with stoichiometric water of crystallization that is part of the formula mass:
- CuSO₄·5H₂O 249.69 vs anhydrous CuSO₄ 159.61 (+56% mass).
- FeSO₄·7H₂O 278.01 vs anhydrous 151.91 (+83% mass).
- MgSO₄·7H₂O 246.47 vs anhydrous 120.37 (+105% mass).
- Na₂CO₃·10H₂O 286.14 vs anhydrous 105.99 (+170% mass).
- EDTA·2H₂O·2Na 372.24 vs anhydrous Na₂EDTA 336.21.
Using the wrong form gives 30-100% errors. The MW values in the calculator presets are anhydrous (the chemical compound itself). For hydrate forms, override with the hydrate MW in custom mode.
Density Sources. For research-grade work, use:
- CRC Handbook of Chemistry and Physics — density tables for binary aqueous solutions of every common reagent.
- International Critical Tables of Numerical Data, Physics, Chemistry and Technology (vol. III).
- Supplier datasheets / Certificates of Analysis (CoA) for the specific lot.
- NIST WebBook for thermophysical-grade data.
- Software: REFPROP (NIST), CRC Handbook online subscription, Sigma-Aldrich solubility/density database.
The Inverse Conversion (M → %). Sometimes the inverse problem arises: given a target molarity and known density, what % do I need? Rearrange: % = (M × MW) / (10 × ρ). Example: target 1.0 M NaOH; ρ ≈ 1.04 g/cm³ for ~1 M aqueous NaOH; % = (1.0 × 40) / (10 × 1.04) = 3.85% w/w. For dilute aqueous solutions (M < 1 mol/L) where ρ ≈ 1 g/cm³: % ≈ (M × MW) / 10. For 1 M glucose: % ≈ (1 × 180.16) / 10 = 18% w/w. References: CRC Handbook of Chemistry and Physics; supplier (Sigma-Aldrich, Fisher, VWR) reagent datasheets; IUPAC Compendium of Chemical Terminology.
Conclusion
Two operational reminders: (1) The most common error is using the wrong density — density varies significantly with concentration (10% HCl ≈ 1.05 g/cm³ vs 37% HCl ≈ 1.19 g/cm³); always use the supplier-specific value for YOUR bottle's exact concentration. (2) The second most common error is hydrate vs anhydrous MW confusion — CuSO₄·5H₂O 249.69 g/mol vs anhydrous CuSO₄ 159.61, MgSO₄·7H₂O 246.47 vs anhydrous 120.37. Always check the bottle for "·nH₂O" notation. For accurate working-solution preparation, follow conversion with C₁V₁ = C₂V₂ dilution math; use a calibrated volumetric flask, not a graduated cylinder, for the final volume adjustment; and always add concentrated acid TO water (never water to concentrated acid) to prevent dangerous heat-of-dilution splashing.
Frequently Asked Questions
What is the Percentage Concentration to Molarity Calculator?
Pro Tip: Pair this with our Molarity Calculator.
What is the formula for percentage to molarity?
How do I convert 37% HCl to molarity?
How do I convert 98% H₂SO₄ to molarity?
How do I convert 50% NaOH to molarity?
What's the molarity of concentrated ammonia?
What's the molarity of concentrated nitric acid?
Why does the calculator have so many solution presets?
Why is solution density important?
How do I find density for an unusual concentration?
What's the inverse conversion (molarity to %)?
Disclaimer
The conversion M = (% × ρ × 10) / MW assumes you know the correct density at YOUR concentration. Density varies significantly with concentration (10% HCl ρ ~1.05 vs 37% HCl ρ ~1.19) — always use the supplier-specific density for your bottle's exact concentration. CRC Handbook density tables cover most aqueous reagents. The MW values in the preset list are anhydrous; for hydrate forms (CuSO₄·5H₂O 249.69 vs anhydrous 159.61) use the form on YOUR bottle label. Strong acids and bases generate heat on dilution — always add concentrated acid TO water (not water to acid) and use heat-resistant glassware. References: CRC Handbook of Chemistry and Physics; supplier (Sigma-Aldrich, Fisher, VWR) reagent datasheets; IUPAC Compendium of Chemical Terminology.