This dilution calculator solves the C1V1 = C2V2 equation for any one unknown — stock concentration, stock volume, final concentration, or final volume. Lab researchers, biotechnology students, and quality control technicians use it daily to prepare working solutions, reagents, and standards from concentrated stocks without doing the algebra by hand.
Model an n-step serial dilution: each tube is diluted by the same factor from the previous one. Enter the starting concentration, the dilution factor per step, and the number of steps.
Inputs: Solve for V1, with C1 = 1 M, C2 = 10 mM, V2 = 50 mL.
Result: V1 = (C2 × V2) / C1 = (0.01 M × 50 mL) / 1 M = 0.5 mL of stock.
You would pipette 0.5 mL of the 1 M Tris-HCl stock into a container, then add diluent up to a total volume of 50 mL (49.5 mL of water or buffer). This gives an accurately prepared 10 mM working solution without wasting concentrated stock.
| Step | 1:2 Series | 1:5 Series | 1:10 Series |
|---|---|---|---|
| Stock (1×) | 1.0 | 1.0 | 1.0 |
| Step 1 | 0.5 | 0.2 | 0.1 |
| Step 2 | 0.25 | 0.04 | 0.01 |
| Step 3 | 0.125 | 0.008 | 0.001 |
| Step 4 | 0.0625 | 0.0016 | 0.0001 |
| Step 5 | 0.03125 | 0.00032 | 0.00001 |
| Step 6 | 0.015625 | 0.000064 | 0.000001 |
How to Use the Dilution Calculator
Select which variable you want to solve for using the "Solve For" buttons. Enter the three known values — the calculator will find the fourth using the C1V1 = C2V2 equation. Units must be consistent: if C1 and C2 are both in M, V1 and V2 must be in the same volume unit.
The Dilution Formula
C1 = Initial (stock) concentration | V1 = Volume of stock solution taken | C2 = Final (desired) concentration | V2 = Final total volume after dilution
The volume of diluent (solvent) to add = V2 − V1
Example Calculations
V1 = (C2 × V2) / C1
V1 = (1 × 100) / 10 = 10 mL
Add 10 mL HCl → make up to 100 mL.
C2 = (C1 × V1) / V2
C2 = (2 × 5) / 50 = 0.2 M
V2 = (C1 × V1) / C2
V2 = (100 × 2) / 10 = 20 mL
C1 = (C2 × V2) / V1
C1 = (0.5 × 50) / 10 = 2.5 M
About Solution Dilution in the Laboratory
Dilution is the process of reducing the concentration of a solute in a solution by adding more solvent. The C1V1 = C2V2 equation is the most fundamental formula in laboratory science, used daily for preparing working solutions from concentrated stocks.
This principle is applied across all areas of biotechnology: preparing antibody dilutions for Western blot, making agarose gels from stock TAE buffer, diluting DMSO stocks of drugs for cell culture assays, and setting up standard curves for ELISA experiments.
Important Notes
When to Use This Calculator
Reach for this tool any time you need to go from a concentrated stock to a working solution. Common scenarios include diluting a 10X PCR buffer down to 1X before setting up a reaction, preparing a 1 µg/mL antibody working dilution from a 1 mg/mL stock for immunostaining, making a 70% ethanol wash solution from absolute ethanol, or diluting a drug stock in DMSO to the final treatment concentration for a cell culture assay. It is equally useful for back-calculating how concentrated a stock must be made if you already know the final volume and concentration you need, which is common when ordering or reconstituting lyophilized reagents.
Common Mistakes to Avoid
- Mixing concentration units. Entering C1 in mg/mL and C2 in M will silently produce a meaningless dilution factor, since the calculator does not convert between molar and mass-based concentration units. Convert both to the same unit family before entering them.
- Confusing V2 with the diluent volume. V2 is the total final volume after dilution, not the amount of water or buffer you add. The diluent volume is V2 minus V1, which the calculator computes for you — don't add V1 worth of solvent on top of V2.
- Forgetting unit prefixes on volume. Pipetting 10 instead of 10 µL is a thousand-fold error. Always double check the unit dropdown next to each volume field matches what you intend to measure on the bench.
- Treating dilution as concentration. If your measured C2 needs to be higher than your available C1, you cannot fix this with more dilution — you need a more concentrated stock or a concentration step instead.
Interpreting Your Results
The highlighted result box shows the value you solved for, along with a complete summary of all four C1V1=C2V2 variables so you can sanity-check the math at a glance. The "Diluent to add" figure tells you exactly how much solvent to pipette to reach your final volume, and the dilution factor (shown as a ratio such as 1:10) tells you how many-fold the original stock was diluted — useful for recording in a lab notebook or comparing against a protocol's specified dilution. If a result looks unexpectedly large or small, it is usually a sign that a unit was selected incorrectly rather than an error in the formula itself.
Frequently Asked Questions
Why can't I get C2 to be greater than C1 in this calculator?
Simple dilution can only ever lower a solution's concentration, never raise it, because you are only adding solvent and never removing it or adding more solute. If your target C2 is higher than your stock C1, you would need a different process such as evaporation, adding more solute, or starting from a more concentrated stock. The calculator blocks this case and returns an error so you don't end up with an impossible or misleading result.
What units should I use for the dilution calculator?
Any unit works as long as C1 and C2 use the same type of concentration unit (for example, both in M, both in mg/mL, or both in %), and V1 and V2 use the same type of volume unit (for example, both in mL or both in µL). The unit dropdowns let you mix display units like µL and mL, and volumes are converted to a common base automatically, but concentration units are not auto-converted, so M and mg/mL cannot be mixed directly.
How do I calculate the volume of diluent to add?
The volume of diluent, usually water or buffer, equals the final volume minus the stock volume you transferred: Diluent = V2 − V1. For example, if you take 10 mL of stock and dilute it to a final volume of 100 mL, you add 90 mL of diluent. This calculator displays the diluent volume automatically alongside the main result so you don't need to subtract it by hand.
What is a dilution factor and how is it different from concentration?
The dilution factor describes how many times a solution has been diluted, expressed as a ratio like 1:10, and is calculated as C1/C2 or equivalently V2/V1. Concentration is the absolute amount of solute per volume, such as 2 M or 5 mg/mL, while the dilution factor is a relative, unitless comparison between the stock and final solution. Two completely different stock concentrations can still share the same dilution factor if they were diluted by the same proportion.
Can I use this calculator for serial dilutions?
This tool solves a single C1V1=C2V2 dilution step, so for a serial dilution you would run the calculation once per step, using the output concentration of one step as the C1 input for the next. If you regularly perform multi-step dilution series, such as preparing a standard curve, BioToolsKit's dedicated Serial Dilution Calculator automates the entire sequence in one pass and is linked below.