Introduction
Molarity tells you how much of a substance is dissolved in a given volume of solution. It is one of the most common ways to describe concentration in chemistry, and you need it for almost every lab calculation. This molarity calculator helps you quickly find any missing value in the molarity equation: concentration, mass, volume, or molecular weight. Just enter three of the four values and leave one blank. The calculator does the rest.
The tool also includes a built-in dilution calculator that uses the C₁V₁ = C₂V₂ formula. This is the standard equation for figuring out how to dilute a stock solution to a lower concentration. Whether you need to know how much solvent to add or what your final volume should be, you can solve for any one of the four dilution variables by filling in the other three. Both calculators support a wide range of units, from picograms to kilograms and from femtomolar to full molar, so they work for tasks in biochemistry, pharmaceutical science, and general chemistry alike.
How to use our Molarity Calculator
This calculator has two sections. The General Molarity Equation Solver finds any unknown variable in the molarity formula when you provide the other three. The Dilution Calculator uses the C₁V₁ = C₂V₂ equation to solve for any one missing dilution value. In each section, fill in three fields and leave one blank, then press Calculate.
General Molarity Equation Solver
Mass: Enter the mass of your solute and pick a unit from the dropdown. Options range from picograms to metric tons, and also include daltons, pounds, and ounces. Leave this field blank if mass is what you want to solve for.
Concentration: Enter the molar concentration of your solution and choose a unit. You can select from molarity units like fM, pM, nM, µM, mM, and M, or use mass concentration units such as g/L, mg/L, ppm, and ppb. Leave this field blank if concentration is what you need to find.
Volume: Enter the volume of your solution and select a unit. Metric options include nanoliters through cubic meters, and imperial options include US gallons, quarts, pints, cups, fluid ounces, and cubic yards, feet, or inches. Leave this field blank if volume is the unknown.
Molecular Weight: Enter the molecular weight of your solute in g/mol or kg/mol. This value is needed for converting between mass and moles. You can look up molecular weights to find the value for your compound. Leave this field blank if molecular weight is what you want to calculate. Note that solving for molecular weight requires concentration to be in molarity units, not mass concentration units.
Dilution Calculator (C₁V₁ = C₂V₂)
C₁ (Initial Concentration): Enter the concentration of your stock or starting solution. Choose from the same molarity and mass concentration units available in the general solver. Leave this blank if the initial concentration is the unknown.
V₁ (Initial Volume): Enter the volume of stock solution you are using or need. Select a metric or imperial volume unit from the dropdown. Leave this blank if you want to find out how much stock solution is required.
C₂ (Final Concentration): Enter the target concentration you want after dilution. Use the same concentration unit options as C₁. Leave this blank if the final concentration is the value you need to determine.
V₂ (Final Volume): Enter the total volume of the diluted solution. Pick a volume unit from the dropdown. Leave this blank if you want to find the final volume. The result will also show you how much solvent to add, calculated as V₂ minus V₁.
What Is Molarity?
Molarity is one of the most common ways to describe the concentration of a solution in chemistry. It tells you how many moles of a solute (the substance being dissolved) are present in one liter of solution. Molarity is written with the unit M (capital M), and a solution labeled "1 M" contains exactly one mole of solute per liter. Because it directly connects the amount of a chemical substance to the volume of liquid it's dissolved in, molarity is essential for lab work, chemical reactions, and many real-world applications like medicine and water treatment.
The Molarity Formula
The core equation for molarity is:
Molarity (C) = Mass (m) ÷ (Molecular Weight (MW) × Volume (V))
This formula has four variables: mass, concentration, volume, and molecular weight. If you know any three of them, you can solve for the fourth. Here's what each variable means:
- Mass (m): The weight of the solute you are dissolving, usually measured in grams or milligrams.
- Molecular Weight (MW): The mass of one mole of the solute, measured in grams per mole (g/mol). You can find this on the periodic table or a chemical's data sheet. For example, table salt (NaCl) has a molecular weight of about 58.44 g/mol. A molecular weight calculator can determine this value from a compound's chemical formula.
- Volume (V): The total volume of the final solution, usually measured in liters or milliliters.
- Concentration (C): The molarity of the solution, measured in mol/L (M).
You can rearrange this formula depending on what you need. For instance, if you want to know how much solute to weigh out, use: Mass = Concentration × Volume × Molecular Weight.
What Is a Dilution and How Does C₁V₁ = C₂V₂ Work?
Dilution is the process of adding more solvent (usually water) to a solution to lower its concentration. The amount of solute stays the same. You're just spreading it across a larger volume. The equation that describes this is:
C₁ × V₁ = C₂ × V₂
- C₁ = the initial (starting) concentration
- V₁ = the initial volume of the concentrated solution
- C₂ = the final (desired) concentration
- V₂ = the final total volume after dilution
This equation works because the total moles of solute before and after dilution are equal. If you know three of these four values, you can calculate the missing one. The calculator above also tells you how much solvent to add, which is simply V₂ − V₁.
Quick Example
Suppose you have a chemical with a molecular weight of 100 g/mol and you dissolve 5 mg of it in 10 mL of water. Using the formula:
Molarity = 0.005 g ÷ (100 g/mol × 0.01 L) = 0.005 M, or 5 mM.
Now imagine you need to dilute that 5 mM solution down to 2 mM. Using C₁V₁ = C₂V₂ with V₁ = 5 mL:
5 mM × 5 mL = 2 mM × V₂ → V₂ = 12.5 mL. You would add 7.5 mL of solvent to your original 5 mL.
Tips for Accurate Results
- Always double-check your units. Mixing up milligrams and grams or milliliters and liters is one of the most common mistakes in concentration calculations.
- Use the molecular weight of the exact form of your chemical. Hydrated salts, for example, weigh more than their anhydrous forms because of the extra water molecules.
- Volume refers to the final solution, not the solvent alone. When making a solution in the lab, dissolve the solute first, then add solvent until you reach the target volume.
- Mass concentration units like ppm and g/L measure mass per volume rather than moles per volume. Converting between these and molarity always requires the molecular weight of the solute.