How to Calculate Solution Dilutions for Real Lab Work

Which scenario do I need?

• Making a fresh working solution from a stock → Classic Dilution (C₁V₁ = C₂V₂)
• Raising the concentration of a solution you already have → Spike Into Existing
• You overshot your target concentration → Back Dilution
• You need an exact final volume, not just a ratio → Dilute to Exact Volume
• Combining two solutions of the same solute at different strengths → Mix Two Solutions

Example 1: Making a working solution from stock

You have a 1000 mM stock solution and need 500 mL of a 50 mM working solution. Open the Classic Dilution panel, solve for V₁, and enter:

• C₁ — stock concentration: 1000 mM
• C₂ — desired concentration: 50 mM
• V₂ — final volume: 500 mL

The result is 25 mL of stock. Add 475 mL of diluent to reach the 500 mL final volume.

Example 2: Spiking an existing solution to a higher concentration

You already have 500 mL of solution at 10 mM, and you want to raise it to 50 mM by adding a 1000 mM stock directly, without starting over. Open Spike Into Existing and enter:

• Mₚ — present concentration: 10 mM
• Vₚ — present volume: 500 mL
• Mₛ — stock concentration: 1000 mM
• Mf — desired final concentration: 50 mM

You need to add 21.05 mL of stock. The final volume becomes 521.05 mL at 50 mM.

Example 3: Fixing an overshoot (back dilution)

You made 200 mL at 250 mM, but your protocol actually needed 100 mM. Open Back Dilution and enter:

• C₁ — current concentration: 250 mM
• V — current volume: 200 mL
• C₂ — target concentration: 100 mM

Add 300 mL of diluent. The final volume becomes 500 mL at exactly 100 mM.

Example 4: Hitting an exact final volume

A gel protocol calls for exactly 200 µL of a 10 mM loading dye working solution, made from a 500 mM stock. Open Dilute to Exact Volume and enter:

• C₁ — stock concentration: 500 mM
• C₂ — desired concentration: 10 mM
• V₂ — exact final volume needed: 200 µL

Take 4 µL of stock and add 196 µL of diluent — exactly 200 µL total at 10 mM.

Example 5: Mixing two solutions together

You combine 200 mL of a 100 mM buffer with 300 mL of a 500 mM buffer of the same solute. What's the resulting concentration? Open Mix Two Solutions and enter:

• M₁: 100 mM, V₁: 200 mL
• M₂: 500 mM, V₂: 300 mL

The final concentration is 340 mM, in a combined 500 mL volume.

Common mistakes to avoid

• Stock weaker than target. In Classic Dilution and Dilute to Exact Volume, your stock concentration (C₁) must be higher than your target (C₂) — you can only dilute down, not up, by adding diluent alone.
• Confusing "final volume" with "diluent volume." V₂ in these calculators is always the total volume after mixing, not the amount of water or buffer you add on top. The diluent volume is V₂ minus V₁.
• Wrong scenario for the situation.If you already have a solution in a tube and want to change its concentration in place, that's Spike Into Existing or Back Dilution — not Classic Dilution, which assumes you're building the solution from scratch.

Frequently asked questions

Can I use these calculators for X-fold dilutions, like 10X to 1X?

Yes — treat the fold notation as a ratio and convert to matching concentration units, or simply express both sides in the same arbitrary units (e.g. treat 10X as "10" and 1X as "1" in the concentration fields); the math is the same either way since C₁V₁ = C₂V₂ only cares about the ratio.

What if I don't know the starting concentration at all?

If you're starting from a dry solute rather than an existing solution, use the Molarity Calculator instead — it calculates concentration from mass, volume, and molar mass.

How do I plan a full dilution series, not just one step?

Use the Serial Dilution Calculator, which builds an entire tube-by-tube series with transfer and diluent volumes for each step.