Calculate serial dilutions, solution concentrations, and mixing ratios
The fundamental dilution formula C1V1 = C2V2 states that the product of initial concentration and volume equals the product of final concentration and volume. This calculator solves for any unknown variable when you provide the other three, making it straightforward to determine how much stock solution or solvent you need for your target concentration and volume.
Accurate dilutions are the foundation of reliable experimental results across chemistry, biology, and clinical diagnostics. An incorrectly prepared standard curve will cascade errors through every measurement that depends on it. In pharmaceutical compounding, even small concentration errors can mean the difference between a therapeutic dose and a toxic one, making precise dilution calculations essential.
Serial dilutions involve repeatedly diluting a solution by a fixed factor, creating a geometric series of concentrations. Each step transfers a set volume into fresh solvent, reducing concentration by the dilution factor. This technique is widely used in microbiology for colony counting, in immunology for antibody titer determination, and in pharmacology for generating dose-response curves across several orders of magnitude.
Always use calibrated pipettes and volumetric glassware rather than graduated cylinders for critical dilutions. Mix thoroughly after each dilution step by vortexing or inverting multiple times to ensure homogeneity. When performing serial dilutions, change pipette tips between each transfer to prevent carryover contamination, and label all tubes clearly before you begin the procedure.
Dilution is the process of decreasing the concentration of a solute in a solution, usually by adding more solvent. This is one of the most common procedures in laboratory work.
Simple Dilution: Mixing a stock solution with solvent to achieve a desired concentration.
Serial Dilution: Making a series of stepwise dilutions from an initial stock solution. Each dilution uses the previous dilution as its starting point.
Mixing Solutions: Combining two solutions of different concentrations to achieve an intermediate concentration.
ā¢ Always add acid to water, never water to acid
ā¢ Mix thoroughly after each dilution
ā¢ Use appropriate pipettes for accuracy
ā¢ Label all dilutions clearly with concentration and date
ā¢ Consider making extra volume to account for pipetting errors
C1V1=C2V2 is the fundamental dilution equation where C1 is the initial concentration, V1 is the initial volume, C2 is the final (desired) concentration, and V2 is the final volume. It works because the amount of solute remains constant before and after dilution. You can solve for any one unknown variable when you know the other three. For example, to find V2, rearrange to V2 = (C1 x V1) / C2.
A serial dilution involves repeatedly diluting a solution by a constant factor. Start with your stock solution and transfer a fixed volume into a tube containing fresh diluent. Mix thoroughly, then transfer the same volume from that tube into the next tube of diluent. Each step reduces the concentration by the dilution factor. For example, a 1:10 serial dilution transfers 1 part solution into 9 parts diluent at each step, creating concentrations of 1/10, 1/100, 1/1000, and so on.
The C1V1=C2V2 equation works with any units as long as you are consistent. Both concentration values (C1 and C2) must use the same unit, such as molarity (M), millimolar (mM), micrograms per milliliter, or percent. Both volume values (V1 and V2) must also share the same unit, such as milliliters or microliters. The equation is unit-agnostic, so mixing units is the most common source of error.