How to dilute a solution step by step
Every dilution obeys C₁V₁ = C₂V₂, because the amount of solute stays the same. You are only adding solvent. C₁ and V₁ are the concentration and volume of the concentrated stock you start with; C₂ and V₂ are the concentration and volume you want to end up with. Rearrange for whatever you are missing (for example, V₁ = C₂V₂ / C₁), measure that much stock, then add solvent until the total volume reaches V₂. The amount of solvent to add is simply V₂ − V₁.
Units just need to match on both sides. Use the same concentration unit for C₁ and C₂, and the same volume unit for V₁ and V₂.
Related tools: Buffer calculator · Antibody dilution calculator · all biochem tools.
Worked example 1: solving for stock volume (the default)
You need 100 mL of a 1 M solution, starting from a 10 M stock. How much stock do you measure out?
Measure 10 mL of the 10 M stock, add 90 mL of solvent, and the result is 100 mL of a 1 M solution. This matches the calculator's default values exactly.
Worked example 2: a real lab dilution
A lab has 5 M NaOH stock and needs 2 L (2000 mL) of 0.1 M NaOH for a titration.
Measure 40 mL of the 5 M stock into a container, then add solvent (typically water, added carefully to concentrated NaOH, never the reverse) up to a total of 2000 mL.
Worked example 3: antibody dilution for Western blot
Antibody dilutions are usually given as a ratio (like "1:1000") rather than a molar concentration, but the same C₁V₁ = C₂V₂ math applies, just treat the undiluted stock as C₁ = 1 and the target dilution as a fraction. You need 10 mL of primary antibody at a 1:1000 dilution for a Western blot.
Pipette 10 µL of antibody stock into 9.99 mL of blocking buffer, in practice, most people just top up to 10 mL total after adding the 10 µL, since the difference is negligible at this dilution factor.
FAQ
Why must units match on both sides?
The equation states that moles of solute don't change on dilution, only true if concentration is in the same unit on both sides and volume is in the same unit on both sides. Mixing M with mM gives an answer off by 1000×.
Does this work for units other than molarity?
Yes, percent (w/v or v/v), mg/mL, ng/µL, normality, anything, as long as it's used consistently. The logic (solute amount is conserved, only solvent is added) doesn't depend on which unit you're tracking.
Can I use this when mixing two solutions together, not just adding solvent?
No. This assumes you're diluting with pure solvent (C = 0). Combining two solutions that both contain solute needs a mass balance instead: C₁V₁ + C₂V₂ = C₃(V₁+V₂), solved for the final concentration C₃.
What's the difference between this and the serial dilution calculator?
This solves one dilution step. The serial dilution calculator chains many identical steps together and tracks concentration and transfer volume at every step of the series.
How do I calculate an antibody dilution like 1:1000?
Same formula, treat the undiluted stock as C₁ = 1 and the target ratio as a fraction (1:1000 → C₂ = 0.001). Solve for V₁ to find how much stock to use, then add diluent up to your target final volume.
Practice problems
1. You have 20 mL of a 3 M stock and want to dilute it to 0.5 M. What final volume do you need?
Show answer
2. You dilute 8 mL of stock up to 200 mL and measure the result at 0.1 M. What was the original stock concentration?