Dilution Calculator
C₁ · V₁ = C₂ · V₂
C₁ — Initial concentration
V₁ — Stock volume to pipette
C₂ — Final concentration
SolvingV₂ — Total final volume
Starting Conditions
About This Tool
What Is the Dilution Formula?
Dilution calculations rest on a single conservation law: the number of moles (or mass) of solute in a solution does not change when you add more solvent. If you take a volume V₁ from a stock at concentration C₁ and dilute it to a total volume V₂, the new concentration C₂ satisfies:
C₁ × V₁ = C₂ × V₂
This equation holds for any consistent pair of concentration units (M, mg/mL, % w/v, etc.) as long as both concentrations use the same basis and both volumes use the same unit. Solve for any one of the four variables by filling in the other three.
Concentration and Volume Units
The calculator supports a wide range of units and handles the conversions automatically.
Molar Concentration Units
• M (mol/L): standard molarity – moles of solute per litre of solution.
• mM: 1 mM = 10⁻³ M. Common in biochemistry for enzyme kinetics.
• µM: 1 µM = 10⁻⁶ M. Typical for receptor binding assays.
• nM: 1 nM = 10⁻⁹ M. Used in high-sensitivity assays, ELISA, and pharmacology.
Mass-Based Concentration Units
• mg/mL: numerically equal to g/L. Widely used for protein and drug concentrations.
• µg/mL: 1 µg/mL = 10⁻³ mg/mL. Used for trace analytes and antibody concentrations.
• g/L: identical to mg/mL numerically (1 g/L = 1 mg/mL).
• % w/v: grams of solute per 100 mL of solution. 1 % w/v = 10 mg/mL.
• % v/v: mL of solute per 100 mL of solution. Used for solvents and buffers.
💡 Cross-unit conversions
To convert between molar (M) and mass units (mg/mL), supply the solute's Molecular Weight (g/mol) in the Optional Parameters. The relationship is: mg/mL = M × MW. For example, 1 M NaCl (MW = 58.44 g/mol) = 58.44 mg/mL.
Stock Purity Correction
Reagents are not always 100 % pure. If the stock bottle states 95 % purity, the actual active concentration is:
C₁_effective = C₁_labeled × (purity% / 100)
Enter the purity percentage in Optional Parameters and the calculator automatically reduces C₁ before solving. This is essential for accurate preparation of standard curves and working solutions from raw chemical stocks.
What Is a Serial Dilution?
A serial dilution creates a geometric concentration series by applying the same dilution factor repeatedly. At each step, a fixed volume V_stock is taken from the previous tube and combined with solvent to reach the target step volume Vstep:
V_stock = Vstep / F V_solvent = Vstep − V_stock C_out = C_in / F
where F is the per-step dilution factor (e.g. 10 for a 1:10 dilution, 2 for a 1:2 dilution). After N steps, the cumulative dilution factor is F^N and the final concentration is Cstart / F^N.
Choosing a Dilution Mode
• Per-step factor + N steps: most straightforward. Enter F (e.g. 10) and the number of tubes. Every tube is diluted identically.
• Target concentration + N steps: enter your desired final concentration and how many steps to use. The calculator computes the per-step factor F = (Cstart/Ctarget)^(1/N) so the series lands exactly on the target.
• Overall factor + N steps: specify total dilution (e.g. 1:1000 in 3 steps) and the calculator splits the burden evenly: F = 1000^(1/3) ≈ 10.
Minimum Pipette Volume Warning
If the calculated stock volume per step is smaller than your pipette's minimum range (commonly 1–5 µL for a standard micropipette), the table highlights that row in amber and a warning is shown. To resolve this, increase the per-step volume (Vstep), reduce the per-step factor, or add more steps so each factor is smaller.
Practical Examples
Example 1 – Preparing a 0.1 M NaCl solution from 1 M stock
Given: C₁ = 1 M, C₂ = 0.1 M, V₂ = 50 mL. Solve for V₁.
V₁ = (C₂ × V₂) / C₁ = (0.1 × 50) / 1 = 5 mL
Pipette 5 mL of 1 M NaCl stock into a 50 mL flask and add 45 mL of water.
Example 2 – 1:10 serial dilution from 1 mM down to 1 nM (3 steps)
Starting at 1 mM with 1 mL per tube and per-step factor = 10:
| Tube | Stock (µL) | Solvent (µL) | Total (mL) | Concentration |
|---|---|---|---|---|
| A | 100 | 900 | 1 | 100 µM |
| B | 100 | 900 | 1 | 10 µM |
| C | 100 | 900 | 1 | 1 µM |
Tips for Accurate Dilutions
• Calibrate pipettes regularly. A 1 % pipette error compounds over serial dilution steps, causing the final concentration to be off by a factor of (1.01)^N.
• Mix thoroughly at each step. Vortex or invert each tube before withdrawing the aliquot for the next step to prevent concentration gradients.
• Pre-wet pipette tips. Aspirate and dispense the solution once before taking the actual aliquot, especially when working with viscous solutions.
• Use the correct temperature. Volume measurements are temperature dependent; perform dilutions at the specified assay temperature.
• Keep stock concentration verified. Measure stock concentration by absorbance (A280, BCA, etc.) rather than relying solely on the label.
Frequently Asked Questions
Yes, Dilution Calculator is totally free :)
Yes, you can install the webapp as PWA.
Yes, any data related to Dilution Calculator only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.
The calculator uses C₁V₁ = C₂V₂, where C₁ is the initial concentration, V₁ is the volume taken from the stock, C₂ is the final concentration, and V₂ is the total final volume. Solve for any one unknown by filling in the other three values.
Supported units include M (mol/L), mM, µM, nM for molar concentrations, and mg/mL, µg/mL, g/L, % w/v, % v/v for mass-based concentrations. When mixing molar and mass units, provide Molecular Weight (g/mol) to enable cross-unit conversions.
A serial dilution creates a series of stepwise dilutions, each using a fixed dilution factor. It is used when a single dilution step would require pipetting impractically small volumes, or when you need a concentration gradient (e.g., standard curves, dose-response assays). Each tube uses an aliquot from the previous tube as its stock.
When the stock solution is not 100 % pure (e.g., a reagent with 95 % purity), the effective C₁ is reduced by the purity factor: C₁_effective = C₁_labeled × (purity % / 100). This correction is applied before solving, so the result accounts for the actual amount of active ingredient.
In serial dilution, this warning appears when the calculated stock volume per step falls below your specified minimum pipettable volume (default 1 µL). Pipetting below this threshold introduces significant relative error. The fix is to increase the per-step total volume, reduce the number of steps, or choose a smaller per-step dilution factor.
Enter Cstart = 1 µM, select mode 'Per-step Factor = 10', and set Steps = 3. The calculator will generate three tubes (A, B, C) each diluted 1:10, reaching 100 nM, 10 nM, and 1 nM. Adjust the per-step volume to ensure pipetted volumes are ≥ 1 µL.