Molarity Calculator — Free Online Concentration Tool

How to Use the Molarity Calculator

1. Select the calculation mode: Choose from four available modes depending on what you need to solve. "Calculate Molarity" finds the concentration when you know the amount of solute and solution volume. "Calculate Moles" determines the amount of solute present. "Calculate Volume" finds the required solution volume. "Dilution" solves C1V1 = C2V2 problems.
2. Enter the known values: For the basic molarity, moles, and volume modes, enter two of the three values and the calculator solves for the third. For dilution mode, select which variable to solve for and enter the other three values.
3. Choose volume units: Toggle between liters and milliliters using the volume unit selector. The calculator handles the conversion internally so you can work in whichever unit is most convenient for your experiment.
4. Review the results: The results panel displays the calculated value along with its unit, the mathematical formula used for transparency, and a contextual explanation that describes what the result means in practical terms.

The dilution mode is especially useful for preparing working solutions from concentrated stock solutions. Select the variable you want to solve for (typically V2 for final volume or V1 for the volume of stock needed), enter the known values, and the calculator provides the answer instantly.

Molarity Formulas

Variables Explained

• M (Molarity): The concentration of a solution expressed in moles of solute per liter of solution. Units are mol/L, commonly written as M (capital letter). A 2 M solution contains 2 moles of solute per liter.
• n (Moles): The amount of substance measured in moles. One mole equals Avogadro's number (6.022 x 10^23) of particles, whether atoms, molecules, or ions.
• V (Volume): The total volume of the solution in liters. This is the final solution volume, not the volume of solvent alone.
• C1, V1: The concentration and volume of the initial (more concentrated) solution before dilution.
• C2, V2: The concentration and volume of the final (diluted) solution after adding solvent.

Step-by-Step Example

Calculate the molarity of a solution containing 4.0 grams of NaOH dissolved in 500 mL of solution:

1. Find the molar mass of NaOH: Na (22.99) + O (16.00) + H (1.008) = 40.00 g/mol
2. Convert grams to moles: n = 4.0 / 40.00 = 0.10 mol
3. Convert volume to liters: V = 500 mL / 1000 = 0.50 L
4. Calculate molarity: M = 0.10 / 0.50 = 0.20 M

The solution has a molarity of 0.20 M, meaning it contains 0.20 moles of NaOH per liter. This is equivalent to 8.0 grams of NaOH per liter. In a titration, 25 mL of this solution would provide 0.005 moles of NaOH.

Practical Examples

Example 1: Nadia's Acid-Base Titration Preparation

Nadia needs to prepare 250 mL of 0.1 M hydrochloric acid (HCl) from a 12 M concentrated stock solution for a titration experiment. Using the dilution equation:

• C1 = 12 M (stock), V1 = unknown, C2 = 0.1 M (target), V2 = 0.250 L
• V1 = C2 x V2 / C1 = 0.1 x 0.250 / 12 = 0.002083 L = 2.083 mL

Nadia carefully pipettes 2.1 mL of concentrated HCl into a 250 mL volumetric flask that already contains about 100 mL of distilled water, then dilutes to the mark. She always adds acid to water, never the reverse, to safely control the exothermic reaction.

Example 2: Marcus's Biology Buffer Solution

Marcus needs to prepare 2 liters of 0.05 M phosphate buffer for a cell culture experiment. He uses monosodium phosphate (NaH2PO4, molar mass = 119.98 g/mol) as the solute:

• Moles needed: n = M x V = 0.05 x 2.0 = 0.10 mol
• Mass required: 0.10 x 119.98 = 11.998 grams

Marcus weighs 12.00 grams of NaH2PO4, dissolves it in approximately 1.8 liters of deionized water, adjusts the pH to 7.4 using NaOH, and then brings the total volume to exactly 2.0 liters. The precise molarity ensures reproducible experimental conditions across his cell culture studies.

Example 3: Dr. Torres's Serial Dilution

Dr. Torres needs a series of five standards for spectrophotometric analysis, ranging from 0.1 M to 0.00625 M, using a 1:2 serial dilution from a 0.1 M CuSO4 stock. She calculates each step:

• Standard 1: 0.1 M (stock solution, no dilution needed)
• Standard 2: 0.1 x 0.5 = 0.05 M (50 mL stock + 50 mL water)
• Standard 3: 0.05 x 0.5 = 0.025 M (50 mL of Std 2 + 50 mL water)
• Standard 4: 0.025 x 0.5 = 0.0125 M (50 mL of Std 3 + 50 mL water)
• Standard 5: 0.0125 x 0.5 = 0.00625 M (50 mL of Std 4 + 50 mL water)

Each dilution uses C1V1 = C2V2 where the dilution factor is 1:2. Serial dilutions are a cornerstone technique in analytical chemistry, microbiology, and pharmacology for creating precise concentration gradients from a single stock solution.

Example 4: Kenji's Electrolyte Solution

Kenji is preparing a 0.15 M potassium chloride (KCl) electrolyte solution for an electrochemistry experiment. He needs 500 mL of solution. KCl has a molar mass of 74.55 g/mol:

• Moles: n = 0.15 x 0.50 = 0.075 mol
• Mass: 0.075 x 74.55 = 5.591 grams

Kenji weighs 5.59 grams of KCl on an analytical balance, transfers it to a 500 mL volumetric flask, adds distilled water to dissolve, and fills to the calibration mark. He can use our molecular weight calculator to verify the molar mass of KCl and other compounds.

Common Solution Concentrations Reference Table

Tips and Complete Guide

Converting Between Concentration Units

Chemistry uses several concentration measures besides molarity. To convert between them: Molarity to mass concentration (g/L), multiply by the molar mass. Molarity to mass percent, use: mass% = (M x molar mass) / (10 x density). Molarity to parts per million (ppm) for dilute aqueous solutions: ppm is approximately equal to molarity x molar mass x 1000. For example, 0.001 M NaCl has a mass concentration of 0.001 x 58.44 = 0.05844 g/L, or about 58.44 ppm. These conversions are essential when working between laboratory protocols (which typically use molarity) and environmental or industrial standards (which often use ppm or mass percent).

Safe Dilution Practices

When diluting concentrated acids, always add acid to water, never water to acid. This fundamental safety rule exists because the dissolution of concentrated acid in water is highly exothermic. Adding water to a large volume of concentrated acid can cause localized boiling, spattering hot acid. By adding acid slowly to a larger volume of water, the heat is absorbed by the bulk water safely. For concentrated sulfuric acid, which has a density of 1.84 g/mL, the heat generated is particularly intense. Always wear appropriate personal protective equipment including safety goggles, lab coat, and acid-resistant gloves. Work in a fume hood when handling volatile acids like hydrochloric and nitric acid.

Molarity in Biological and Medical Applications

Biological applications frequently use millimolar (mM) and micromolar (uM) concentrations. Cell culture media, enzyme assays, and drug concentrations are commonly expressed in these units. For example, a typical therapeutic drug concentration might be 10 uM (0.00001 M), while a buffer solution is 50 mM (0.05 M). When preparing biological solutions, sterile technique is essential in addition to concentration accuracy. Many biological buffers have specific pH requirements, so after dissolving the solute and adjusting the volume, pH adjustment with dilute acid or base is typically the final preparation step.

Accuracy and Significant Figures

The accuracy of a molarity calculation depends on the precision of the measurements. An analytical balance measuring to 0.0001 g combined with a volumetric flask accurate to 0.01% can produce solutions accurate to four significant figures. For routine work, measuring to three significant figures is usually sufficient. When diluting, each step introduces small errors that compound — a serial dilution through five steps has more uncertainty than a single direct dilution. For the highest accuracy, prepare solutions by direct weighing whenever possible rather than diluting from stock solutions, and calibrate your volumetric glassware at the temperature at which it will be used.

Common Mistakes to Avoid

• Confusing solution volume with solvent volume: Molarity is defined as moles per liter of solution, not moles per liter of solvent. When dissolving a solid in water, the final volume may differ from the initial water volume, especially for concentrated solutions.
• Mixing up milliliters and liters: The standard molarity formula uses liters. Forgetting to convert 250 mL to 0.250 L before dividing produces an answer 1,000 times too large. Our calculator handles this conversion for you when you select the mL unit option.
• Ignoring temperature effects: Volumetric flasks are calibrated at 20 degrees Celsius. Preparing solutions at significantly different temperatures will affect the actual concentration. For analytical work, allow solutions to equilibrate to the calibration temperature before making the final volume adjustment.
• Adding water to concentrated acid: Always add acid to water during dilutions. Reversing this order can cause dangerous spattering due to the intense exothermic reaction, especially with sulfuric acid.
• Assuming volume additivity: When mixing two liquids, the total volume may not equal the sum of individual volumes. For example, mixing 50 mL of ethanol with 50 mL of water produces approximately 96.4 mL of solution, not 100 mL, due to molecular interactions between water and ethanol.

Frequently Asked Questions