💧 Dilution Calculator

M₁V₁ = M₂V₂ — Solve for any variable.

Solve for

M₁ — Stock Molarity (mol/L)

V₁ — Stock Volume (mL)

M₂ — Final Molarity (mol/L)

V₂ — Final Volume (mL)

—mL

Result

How to Use This Calculator

This tool solves for any one variable in the dilution equation M₁V₁ = M₂V₂. Pick which quantity you need to find, enter the three known values, and click Calculate. All volumes should use the same unit (millilitres is standard for lab work), and molarity is always in mol/L.

Select which variable to solve for: the stock volume V₁, stock molarity M₁, final volume V₂, or final molarity M₂.

Enter the three known values. For example, to prepare a dilute solution you usually know M₁ (the label on the stock bottle), your target M₂, and the total volume V₂ you need.

Click Calculate. The result tells you how much stock to measure out, or what concentration you will end up with.

In the lab: pipette V₁ of stock into a volumetric flask, then add solvent up to the V₂ mark. Always add acid to water, never the reverse.

The Dilution Equation

M₁V₁ = M₂V₂ V₁ = M₂V₂ / M₁ M₂ = M₁V₁ / V₂

M₁ and V₁ are the molarity and volume of the concentrated stock solution. M₂ and V₂ are the molarity and volume of the diluted solution you want to prepare. The equation works because moles of solute are conserved when you add more solvent.

Worked Examples

Prepare 100 mL of 0.1 M HCl from 12 M stockV₁ = (0.1 × 100) / 12 = 0.83 mL

Prepare 250 mL of 0.5 M NaOH from 2 M stockV₁ = (0.5 × 250) / 2 = 62.5 mL

Final concentration after adding 10 mL of 6 M H₂SO₄ to 990 mL waterM₂ = (6 × 10) / 1000 = 0.060 M

Prepare 500 mL of 1.5 M glucose from 3 M stockV₁ = (1.5 × 500) / 3 = 250 mL

Where This Calculation Comes Up

Dilution calculations are one of the most common tasks in any wet chemistry lab. When you open a bottle of concentrated hydrochloric acid, it is typically 12 M. Nobody works with 12 M HCl directly for most experiments. Preparing a 0.1 M working solution requires measuring a small volume of stock and diluting it to the correct total volume in a calibrated flask. Getting this calculation wrong can mean your titration end-points will be off, or your cell cultures will receive the wrong drug concentration.

The same calculation applies whenever you make serial dilutions for a standard curve in spectrophotometry, or when a biochemistry protocol tells you to make a 1-in-10 or 1-in-100 dilution of a sample before measuring absorbance. If you start with a 5 mg/mL protein stock and need a 0.1 mg/mL working concentration in 1 mL total volume, you add 20 µL of stock and 980 µL of buffer. M₁V₁ = M₂V₂ handles all of these cases the same way.

Frequently Asked Questions

What is the dilution equation?

M1V1 = M2V2, where M1 and V1 are the initial molarity and volume, and M2 and V2 are the final molarity and volume.

How do I prepare 100 mL of 0.1 M HCl from 12 M stock?

V1 = M2V2/M1 = (0.1×100)/12 = 0.833 mL. Take 0.833 mL of concentrated HCl and dilute to 100 mL.

What units should I use?

Any consistent volume units work (mL, L) as long as V1 and V2 use the same unit. Molarity is always in mol/L.

Why does M1V1 = M2V2?

Moles of solute are conserved during dilution: n = M×V is constant regardless of how much water is added.

Can I solve for any variable?

Yes! This calculator solves for M1, V1, M2, or V2 given the other three values.