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Molarity Calculator

Find the molarity of a solution from moles of solute and volume of solution. Also includes a dilution calculator using C1V1 = C2V2 to determine how to dilute a stock solution.

Molarity is the chemistry workhorse unit for solution concentration: moles of solute per liter of solution. A "1 M" (1 molar) sodium chloride solution contains 1 mole of NaCl (58.44 g) dissolved in enough water to make 1 liter of total solution. Note "of solution," not "of water" — the volume measured is the final mixed volume, which is slightly different from the water volume because dissolved solutes change the volume.

This calculator handles two of the most common solution-prep problems. The first is computing molarity from a known moles and volume (or back-solving for either). The second is the dilution equation C₁V₁ = C₂V₂, which describes the relationship between a concentrated stock solution and a more dilute working solution. Given any three of the four variables, the calculator solves for the fourth.

Solutions and dilutions show up in nearly every wet-lab discipline: chemistry labs, biology buffer prep, brewing chemistry, medical drug formulation, pool chemistry, fertilizer mixing. The math is identical; only the units and starting materials change. Mastering this one calculator buys you confidence across all of them.

Inputs

For molarity calculation

For molarity calculation

For dilution calculation

For dilution (leave 0 to solve for V1)

For dilution calculation

For dilution calculation

Results

Molarity

0.5000 M

Molarity (mM)

500.00 mM

Molarity Results

ParameterValue
Moles of Solute0.500000 mol
Moles (mmol)500.0000 mmol
Volume1.0000 L (1000.0 mL)
Molarity0.500000 M
Molarity (mM)500.0000 mM
Concentration (g/L)Depends on molar mass
FormulaM = mol / L
Last updated:

Formula

**Molarity:** M = moles_solute / volume_solution_L Units: mol/L (commonly written as "M" or "mol/L"). **Reverse-solving:** - moles = M × V_L - V_L = moles / M - mass_g = M × V_L × molar_mass_g_per_mol **Dilution equation (C₁V₁ = C₂V₂):** If you take volume V₁ of a stock at concentration C₁, and dilute it to total volume V₂, the new concentration is: C₂ = (C₁ × V₁) / V₂ Solve for any one given the other three: - V₁ = (C₂ × V₂) / C₁ (how much stock do I take?) - V₂ = (C₁ × V₁) / C₂ (what total volume to dilute to?) - C₂ = (C₁ × V₁) / V₂ (final concentration check) - C₁ = (C₂ × V₂) / V₁ (back-calculate stock concentration) **Important: the units of V₁ and V₂ must match.** They cancel in the equation, so use mL/mL or L/L — just be consistent. **Example: dilute 6 M HCl stock to 1 M working solution** - Want 300 mL of 1 M (C₂ = 1 M, V₂ = 300 mL) - Stock: C₁ = 6 M - V₁ = (1 × 300) / 6 = **50 mL stock + 250 mL water** (Always add stock to water, not water to stock, for safety — especially for strong acids.) **Example: starting molarity calculation** - 0.500 mol NaCl in 1.00 L solution = 0.500 M - 0.250 mol NaOH in 0.500 L solution = 0.500 M - 5.00 g NaCl (58.44 g/mol = 0.0856 mol) in 100 mL (0.100 L) = 0.856 M **Other concentration units (related but different):** - **Molality (m)**: moles solute per kg solvent (not solution). Used in colligative-property calculations. - **Mass percent (%w/w)**: grams solute per 100 g solution. - **Volume percent (%v/v)**: mL solute per 100 mL solution (for liquid–liquid). - **ppm (parts per million)**: mg solute per L solution for dilute aqueous solutions. 1 ppm ≈ 1 mg/L = 10⁻⁶ M for dilute solutes. - **Normality (N)**: equivalents per liter; depends on the reaction (acid-base, redox).

How to use this calculator

  1. For molarity: enter moles of solute and volume in liters. The result is M = mol/L.
  2. To convert mass to moles: moles = mass(g) / molar_mass(g/mol). Use the molar mass calculator for compound weights.
  3. For dilution: enter any three of C₁, V₁, C₂, V₂ and solve for the fourth.
  4. Make sure V₁ and V₂ use the same units (both mL or both L). The equation cancels them.
  5. For sequential dilutions (serial dilution), apply C₁V₁ = C₂V₂ step by step. A 1:10 dilution drops concentration 10×; three serial 1:10 dilutions drop it 1000×.
  6. Always add acid to water, never the reverse — concentrated acid + water releases heat that can splash the strong acid out of the container.

Worked examples

Preparing a NaOH titration solution

**Scenario:** You need 250 mL of 0.10 M NaOH for an acid-base titration lab. **Calculation:** Moles needed = 0.10 mol/L × 0.250 L = 0.025 mol. Mass NaOH = 0.025 × 40.00 g/mol = 1.000 g. Weigh 1.00 g of NaOH, dissolve in ~200 mL water in a 250 mL volumetric flask, then fill to the mark. **Result:** 250 mL of 0.10 M NaOH ready for titration. NaOH is hygroscopic — weigh quickly and use within a few hours. For precise work, standardize against a primary standard (potassium hydrogen phthalate) to determine actual concentration.

Diluting stock acid for benchtop work

**Scenario:** Concentrated HCl is ~12 M. You need 100 mL of 3 M HCl for an extraction. **Calculation:** C₁V₁ = C₂V₂ → V₁ = (3 × 100) / 12 = 25 mL stock HCl. Add to ~70 mL of water in a flask, mix, then fill to 100 mL total. **Result:** 25 mL conc HCl into water, dilute to 100 mL total = 3 M HCl. Stock HCl fumes — work in a fume hood. Always pour acid into water (exothermic; water absorbs heat without splashing).

Serial dilution for biology assay

**Scenario:** You have a 1 mM stock of a fluorescent probe and need a series of dilutions for a standard curve: 100 µM, 10 µM, 1 µM, 100 nM. **Calculation:** Use 1:10 serial dilutions. Start with 100 µL of 1 mM stock + 900 µL diluent = 100 µM. Take 100 µL of that + 900 µL diluent = 10 µM. Repeat for 1 µM, then 100 nM. Each tube ends at 1 mL total volume. **Result:** 5 standards (1 mM, 100 µM, 10 µM, 1 µM, 100 nM) made with minimal stock consumption. Serial dilution is more accurate than parallel dilution for very dilute standards because pipetting errors are smaller at moderate volumes.

When to use this calculator

**Use molarity and dilution math whenever you prepare solutions or work with concentrations:**

- **Chemistry lab homework**: stoichiometry, titration, equilibrium problems all rest on accurate molar concentrations. - **Biology buffer prep**: PBS, Tris, citrate, phosphate buffers — all specified by molarity, often diluted from concentrated stocks. - **Pharmacy / medicine**: IV bag concentrations, drug stocks diluted to working ranges, mg/mL to mol/L conversions. - **Brewing chemistry**: water salt additions (gypsum, calcium chloride) often calculated as ppm or mM. - **Aquarium chemistry**: ammonia, nitrate, phosphate test kits report in mg/L, dosing in mol or equivalents. - **Industrial process control**: feed-stream concentrations, dilution to safety thresholds. - **Pool chemistry**: chlorine in ppm (mg/L), sodium carbonate dosing in mol per pool volume.

**Practical solution-prep workflow:**

1. **Pick the target concentration and volume** based on the experiment. 2. **Choose the lowest-effort dilution path** — usually from a 10× or 100× stock to working solution. 3. **Calculate stock volume needed**: V₁ = C₂V₂ / C₁. 4. **Plan the order**: water first, then stock (especially for acids/bases). For salts, dissolve in less than final volume, then top up. 5. **Use a volumetric flask** for accuracy. Graduated cylinders are ±5%; volumetric flasks are ±0.1%. 6. **Mix thoroughly** by inversion or stirring before use. 7. **Label**: name, concentration, date, preparer initials.

**When NOT to use molarity:**

- **Colligative properties** (freezing point depression, osmotic pressure, vapor pressure): use molality (mol/kg solvent), not molarity. - **Acid-base equivalents for redox**: normality (eq/L) may be more useful than molarity. - **Aqueous–organic mixtures**: volume contraction on mixing means measured volume ≠ sum of components. - **Very dilute trace work**: ppm, ppb, and ng/mL are more practical than tiny decimal molarities.

Common mistakes to avoid

  • Using "volume of water" instead of "volume of solution" in molarity. For accurate work, dissolve in less than final volume, then top up to the mark in a volumetric flask.
  • Forgetting unit consistency in C₁V₁ = C₂V₂. Volumes must match (mL/mL or L/L); concentrations must match (M/M or mM/mM).
  • Adding water to concentrated acid. Always add acid to water; the reverse causes splashing from rapid heat release.
  • Confusing molarity (M, mol/L solution) with molality (m, mol/kg solvent). They're only close for dilute aqueous solutions; very different in concentrated or organic systems.
  • Treating 50% w/w stock as if it were 50% v/v or 50% molar. Concentration units must match across calculations.
  • Estimating mass from "scoop and weigh" instead of weighing exactly. Hygroscopic compounds (NaOH, KOH) gain water from air rapidly — weigh fast and stopper.
  • Forgetting that "1 M HCl" stock from a lab supplier might actually be 1.0 ± 5% — standardize for any quantitative work.

Frequently Asked Questions

Sources & further reading

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