Molarity (M) is the number of moles of solute dissolved per liter of solution. Formula: M = moles / volume (L). A 1 M NaCl solution contains 58.44 g of NaCl per liter.

How do you dilute a solution using C1V1 = C2V2?

The dilution equation C1V1 = C2V2 states that concentration times volume is conserved. To find the final volume: V2 = (C1 × V1) / C2. For example, diluting 6M HCl (100 mL) to 0.5M gives V2 = (6 × 0.1) / 0.5 = 1.2 L total.

What is the difference between molarity and molality?

Molarity (M) is moles of solute per liter of solution — it changes with temperature because liquids expand. Molality (m) is moles of solute per kilogram of solvent — it is temperature-independent. Use molarity for most lab calculations and molality for colligative properties like boiling point elevation.

How does serial dilution work?

In serial dilution you apply the same dilution factor repeatedly. Each step reduces the concentration by the factor. For a 1:10 serial dilution starting at 1 M: step 1 = 0.1 M, step 2 = 0.01 M, step 3 = 0.001 M, and so on. It is used in microbiology, pharmacology, and analytical chemistry.

Concentration & Dilution Calculator

Solve for

Quick-fill molar mass

M = n / V

Moles of Solute (mol)

Volume of Solution (L)

Molar Mass (g/mol) optional

n = M × V

Molarity (M)

Volume of Solution (L)

Molar Mass (g/mol) optional

V = n / M

Moles of Solute (mol)

Molarity (M)

Molar Mass (g/mol) optional

C₁V₁ = C₂V₂ → solve for V₂

C₁ — Initial Conc. (M)

V₁ — Initial Volume (L)

C₂ — Final Conc. (M)

Molarity

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Grams of Solute —

Millimoles —

Volume (mL) —

Molarity vs. Volume (at current moles)

Serial Dilution Series

Each step applies the same dilution factor to the previous concentration.

Starting Concentration (M)

Dilution Factor (e.g. 10 for 1:10)

Number of Steps

Step	Concentration (M)	Scientific Notation	Log₁₀(C)

Log-Scale Dilution Series

How do you calculate molarity?

Molarity (M) = moles of solute ÷ liters of solution. For example, 0.5 mol of solute in 0.5 L of final solution gives a 1.0 M solution. To convert from grams, divide mass by molar mass first (moles = grams ÷ g/mol).

3 min read 4 steps 6 terms 2 examples 6 FAQs M = n / V · n = M × V · V = n / M

Calculation only: C₁V₁ = C₂V₂.

General reference Written by Calculover Editorial Team · Updated 2026-07-31 · 2 sources

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Walk-through

How to Use This Calculator

4 steps

Select a Calculation Mode

Choose what you want to find: Molarity (M = n/V), Moles of solute (n = M × V), Volume of solution (V = n/M), or Dilution (C₁V₁ = C₂V₂). Each mode hides irrelevant inputs and solves directly for the selected unknown.

Enter Your Values

Input the known quantities. For molarity mode: moles of solute and volume in liters. Optionally enter the molar mass to see the mass in grams. For dilution mode: initial concentration (C₁), initial volume (V₁), and target concentration (C₂) — the calculator finds the final volume (V₂).

Dilution mass balance

Calculation only: C₁V₁ = C₂V₂. Final solution volume is not initial solvent volume. Volume additivity is an assumption, not a chemical handling protocol.

Plan Serial Dilutions

Use the Serial Dilution tab to plan multi-step dilution series. Enter the starting concentration, dilution factor, and number of steps. The calculator generates a table of concentration at each step in both decimal and scientific notation, with a log₁₀ chart for visualizing the exponential decrease.

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Reference

Formula & Methodology

3 formulas

Molarity

M = n / V · n = M × V · V = n / M

Molarity (M) is the standard unit of concentration in aqueous chemistry: moles of solute per liter of solution. The three forms solve for M, moles (n), or volume (V) depending on which two quantities are known. To convert moles to grams: mass (g) = moles × molar mass (g/mol). A 1 M NaCl solution contains 58.44 g of NaCl per liter of solution.

Dilution

C₁V₁ = C₂V₂

The dilution model conserves n = C₁V₁ = C₂V₂ and solves V₁ = C₂V₂/C₁ for C₁ > 0. A target above the stock concentration is outside dilution-only arithmetic. V₂ − V₁ is a calculated volume difference under an additive-volume assumption, not an instruction for combining substances.

Serial Dilution

Cₙ = C₀ / Fⁿ (where F = dilution factor, n = step number)

Serial dilution applies the same dilution factor repeatedly. Starting from concentration C₀, after n steps with factor F the concentration is C₀ / Fⁿ. A 1:10 serial dilution from 1 M produces 0.1 M, 0.01 M, 0.001 M, etc. In log₁₀ terms, concentration decreases linearly with step count — each step subtracts log₁₀(F) from the log concentration. Serial dilutions are used in microbiology for cell counting and in pharmacology for dose-response curves.

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General reference

Trust, Methodology & Sources

Written by Calculover Editorial Team · Updated 2026-07-31 · 2 sources

Editorial accountability

Author: Calculover Editorial Team - Editor

Owner: Calculover Editorial Team - Editorial owner

Last reviewed: 2026-07-31

Last verified: 2026-07-31

Methodology

Assumption: All formulas follow IUPAC recommendations for solution chemistry. Calculations assume ideal solution behavior — real solutions at high concentrations or with strong ionic interactions may deviate. Activity coefficients are not applied.

Limitations & guidance

Always verify calculations independently before use in laboratory, clinical, or industrial settings. This tool is provided for educational purposes.

Professional guidance:

Primary sources

IUPAC Gold Book — Amount concentration (molarity)

ACS Chemical Safety — Acid Handling Guidelines

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Glossary

Key Terms Explained

6 terms

Molarity (M) M = n/V; n = M×V; V = n/M. Calculation only: C₁V₁ = C₂V₂. Final solution volume is not initial solvent volume. Volume additivity is an assumption, not a chemical handling protocol.

Moles (mol) The SI unit of chemical amount: 6.022 × 10²³ particles (Avogadro's number). Converting between moles and grams requires the molar mass: moles = mass / molar mass. For NaCl (molar mass 58.44 g/mol), 117 grams = 2 moles. The mole concept allows chemists to count atoms and molecules in practical lab quantities.

Stock Solution A stock concentration is the supplied starting value C₁ in the conserved-amount model. The calculator uses this value only for arithmetic; it does not specify how a stock solution is prepared or handled.

Dilution Factor The ratio of the initial concentration to the final concentration (C₁/C₂). A dilution factor of 10 means the final solution is 10 times less concentrated than the stock. Expressed as 1:10 in microbiological notation. The total fold-dilution of a serial dilution equals the dilution factor raised to the number of steps: 10⁶ for a 1:10 dilution carried out 6 times.

Solute The substance dissolved in a solution. In a NaCl solution, NaCl is the solute and water is the solvent. Concentration (molarity) measures the amount of solute relative to the total volume of solution — not just the volume of solvent added.

Molar Mass The mass of one mole of a substance in grams per mole (g/mol), numerically equal to the atomic or molecular weight in atomic mass units. Used to convert between moles and grams. Examples: NaCl = 58.44 g/mol, glucose (C₆H₁₂O₆) = 180.16 g/mol, H₂SO₄ = 98.08 g/mol. Molar mass is obtained by summing the atomic weights of all atoms in the formula.

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Scenarios

Real-World Examples

2 worked examples

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Synthetic amount example

Molarity Calculation

Moles of NaCl 0.25 mol Volume 0.5 L (500 mL) Molar Mass of NaCl 58.44 g/mol

M = 0.25 mol / 0.5 L = 0.5 mol/L; m = 0.25 mol × 58.44 g/mol = 14.61 g. Calculation only: C₁V₁ = C₂V₂. Final solution volume is not initial solvent volume. Volume additivity is an assumption, not a chemical handling protocol.

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Synthetic conserved-amount example

Dilution (C₁V₁ = C₂V₂)

C₁ (stock) 6 mol/L C₂ (target) 0.5 M V₂ (target volume) 1 L

V₁ = (0.5 × 1) / 6 L = 1/12 L ≈ 83.3333333333 mL; F = 12; C₁V₁ = C₂V₂ = 0.5 mol. Calculation only: C₁V₁ = C₂V₂. Final solution volume is not initial solvent volume. Volume additivity is an assumption, not a chemical handling protocol.

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Reference

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Use either format to cite this calculator in a paper, report, or resource list.

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Deep Dive

Concentration arithmetic and measurement bases

3 chapters · 3 min read

Calculation only: C₁V₁ = C₂V₂. Final solution volume is not initial solvent volume. Volume additivity is an assumption, not a chemical handling protocol.

Amount and final solution volume

Molarity divides solute amount by final solution volume: M = n/V. For n = 0.25 mol and V = 0.5 L, M = 0.5 mol/L. A volume stated as initial solvent alone is a different measurement and cannot silently replace final solution volume.

Conserved amount in the dilution model

Indexed concentration schedules

For an indexed schedule Cₙ = C₀/Fⁿ, step zero is the initial concentration and n counts transitions. With C₀ = 1 mol/L and F = 5, the first three rows are 1, 0.2 and 0.04 mol/L. A logarithmic plot excludes zero concentrations; its exact numeric table remains available.

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Questions

Frequently Asked Questions

6 questions

What is molarity and how is it different from molality?+

Molarity (M) = moles of solute / liters of solution. Molality (m) = moles of solute / kilograms of solvent. Molarity is more common in lab work because measuring volume is easier than weighing solvent. Molality is temperature-independent because mass doesn't change with temperature; molarity changes slightly as solutions expand and contract. For dilute aqueous solutions at room temperature, they are nearly equal numerically.

How do I use the dilution equation C₁V₁ = C₂V₂?+

V₁ = C₂V₂/C₁. Calculation only: C₁V₁ = C₂V₂. Final solution volume is not initial solvent volume. Volume additivity is an assumption, not a chemical handling protocol.

How do I convert moles to grams?+

Mass (g) = moles × molar mass (g/mol). Find the molar mass by summing atomic weights from the periodic table. NaCl: Na (22.99) + Cl (35.45) = 58.44 g/mol. So 0.5 mol NaCl = 0.5 × 58.44 = 29.22 g. Conversely, moles = mass / molar mass: 100 g of NaCl = 100 / 58.44 = 1.71 mol.

What is a serial dilution and when do I use it?+

What does a 1:10 dilution mean?+

Cₙ = C₀/Fⁿ; F = C₀/C₁. Calculation only: C₁V₁ = C₂V₂. Final solution volume is not initial solvent volume. Volume additivity is an assumption, not a chemical handling protocol.

How do I calculate the concentration of a series of serial dilutions?+

Cₙ = C₀ / Fⁿ, where C₀ is the starting concentration, F is the dilution factor per step, and n is the step number. For a 1 M stock with 1:10 dilutions: Step 1 = 0.1 M, Step 2 = 0.01 M, Step 3 = 0.001 M, Step 6 = 10⁻⁶ M. In log₁₀ terms: log₁₀(Cₙ) = log₁₀(C₀) − n × log₁₀(F). For 1:10 dilutions: each step decreases log₁₀(C) by exactly 1.

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Concentration & Dilution Calculator

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How to Use This Calculator

Select a Calculation Mode

Enter Your Values

Dilution mass balance

Plan Serial Dilutions

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Key Terms Explained

Real-World Examples

Synthetic amount example

Synthetic conserved-amount example

Cite This Calculator

Concentration arithmetic and measurement bases

Amount and final solution volume

Conserved amount in the dilution model

Indexed concentration schedules

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Concentration & Dilution Calculator

How to Use This Calculator

Select a Calculation Mode

Enter Your Values

Dilution mass balance

Plan Serial Dilutions

Formula & Methodology

Trust, Methodology & Sources

Key Terms Explained

Real-World Examples

Cite This Calculator

Concentration arithmetic and measurement bases

Amount and final solution volume

Conserved amount in the dilution model

Indexed concentration schedules

Frequently Asked Questions

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