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Pharmaceutical Calculators · Lab & GMP Compounding

Dilution Calculator: C1V1=C2V2

Calculate stock solution volume and diluent needed using the conservation-of-mass dilution formula. Built for pharma labs, HPLC sample prep, buffer preparation, and formulation R&D.

Quick Answer

The dilution formula C1V1 = C2V2 states that initial concentration times initial volume equals final concentration times final volume, based on conservation of mass. Rearranged as V1 = (C2 × V2) / C1, it tells you how much stock solution to take and how much diluent to add. Pharmaceutical and analytical labs use this equation for buffer prep, HPLC sample dilution, formulation R&D, and GMP compounding when C1 and C2 share the same concentration units.

Formula
C1 × V1 = C2 × V2
C1 = Stock concentration    V1 = Volume of stock needed (solved)
C2 = Target concentration    V2 = Total final volume desired
V1 = (C2 × V2) / C1

Enter Values

Enter stock concentration (C1), target concentration (C2), and final volume (V2). C1 and C2 must use the same unit.

Concentrations
Target volume
Stock Volume (V1)
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Diluent to Add
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Dilution Factor
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×
Verification
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How to Use

1
Enter your stock solution concentration (C1) and select its unit (mg/mL, μg/mL, etc.).
2
Enter your desired final concentration (C2) using the same unit as C1. The target must be lower than the stock concentration.
3
Enter the total final volume you need to prepare (V2) and choose your volume unit (mL, L, or μL).
4
Click Calculate — instantly see the volume of stock to take (V1), volume of diluent to add, dilution factor, and a concentration verification.

Worked Example

Example Calculation

You have a 100 mg/mL stock solution and need 10 mL of a 5 mg/mL solution:

V1 = (C2 × V2) / C1 = (5 × 10) / 100 = 0.5 mL of stock

Diluent = V2 − V1 = 10 − 0.5 = 9.5 mL of diluent

Dilution factor = C1/C2 = 100/5 = 20×

About the C1V1=C2V2 Formula

The dilution equation C1V1 = C2V2 is derived from the conservation of mass principle: the total amount of solute (in moles or mass) does not change when you add diluent to a solution. Since concentration = amount / volume, multiplying each side's concentration by its volume yields the total amount of solute, which must be equal before and after dilution.

This formula is universally applicable across pharmaceutical, clinical, and research settings — from preparing IV infusion solutions and HPLC mobile phases to diluting stock reagents for cell culture assays. The only requirement is that C1 and C2 are expressed in the same units.

For serial or step-wise dilutions (where a diluted solution is diluted again), use the Serial Dilution Calculator.

Pharma & laboratory context

GMP compounding and QC laboratories rely on documented C1V1=C2V2 calculations for buffer preparation, standard solution prep, and release testing. Under USP General Chapter <795> and <797>, compounded preparations require accurate concentration verification, qualified equipment, and batch documentation — especially when dilutions affect patient-facing doses or stability.

Formulation R&D teams use single-step dilution for prototype solutions, excipient compatibility studies, and pre-formulation screening. When concentrations must span several orders of magnitude — for example calibration standards or potency assays — combine this tool with the Serial Dilution Calculator. Convert mass-based inputs to molarity with the Molarity Calculator, validate analytical range with the LOD/LOQ Calculator, and prepare reagents step-by-step with the Solution Preparation Calculator.

HPLC and LC-MS workflows dilute extracted or stock samples to bring analyte levels within the validated calibration curve. Match diluent composition to sample matrix when possible to avoid peak shape changes or ion suppression. For percent w/v or w/w reagents, confirm both concentrations use the same basis before applying C1V1=C2V2.

Evidence & sources

Frequently Asked Questions

C1V1=C2V2 is the dilution formula stating that initial concentration multiplied by initial volume equals final concentration multiplied by final volume. It is derived from the conservation of mass principle — the total amount of solute remains constant during dilution. Rearranged: V1 = (C2 × V2) / C1, which tells you how much stock solution to take.
The dilution factor is the ratio of the final volume to the initial volume (V2/V1), or equivalently the ratio of initial to final concentration (C1/C2). For example, a 1:10 dilution has a dilution factor of 10×, meaning the final solution is 10 times less concentrated than the stock.
Use a single C1V1=C2V2 dilution when the required dilution factor is modest and can be achieved accurately in one step. Use serial dilution when you need very large dilution factors, calibration curves spanning multiple orders of magnitude, or when pipetting very small stock volumes would exceed instrument precision. See our Serial Dilution Calculator for step-wise concentration series.
This calculator works with any concentration unit — mg/mL, μg/mL, mg/L, %, mol/L, or mmol/L — as long as C1 and C2 are expressed in the same unit. Volume can be entered in mL, L, or μL and is converted automatically. The key requirement is unit consistency between the two concentration inputs.
The underlying mathematics — C1V1=C2V2 — is identical. However, in pharmaceutical settings, exact concentration accuracy is critical for patient safety, and sterility must be maintained throughout the process. Pharmaceutical dilutions are typically performed under GMP conditions using validated equipment, with documented calculations, qualified diluents, and batch records.
Dilution reduces the concentration of a solute that is already dissolved in solution by adding more solvent. Dissolution is the process of dissolving a solid (or gas) into a solvent to create a solution from scratch. For example, adding water to a 100 mg/mL drug solution is dilution; dissolving a 100 mg tablet into 1 mL of water is dissolution.
Mathematically yes, but practically large single-step dilutions (for example 10,000×) often require transferring microliter stock volumes that exceed pipette accuracy. For dilution factors above roughly 100×, serial dilution in two or more steps usually improves precision because each step uses manageable transfer volumes. Combine this calculator for the final target step with the Serial Dilution Calculator for intermediate steps.
Percent solutions express concentration as parts per hundred — typically % w/v (grams solute per 100 mL) or % v/v (mL solute per 100 mL). As long as C1 and C2 use the same percent basis, C1V1=C2V2 applies directly. For example, diluting 10% w/v stock to 0.5% w/v is a 20× dilution factor. Do not mix % w/v with % w/w without converting to a common mass or volume basis first.
When concentrations are expressed in mol/L or mmol/L, C1V1=C2V2 still applies because moles of solute are conserved. If you know the solute molecular weight, convert mass-based concentrations to molarity first using our Molarity Calculator, then apply the dilution equation. Molarity-based dilution is standard for reagent prep, buffer design, and stoichiometric reactions.
Relative error in the final concentration propagates from uncertainties in C1, V1 transfer, and V2. Small absolute errors in micropipette delivery become large relative errors at high dilution factors. Use calibrated pipettes within their optimal volume range, prepare solutions gravimetrically when critical, and document balance and pipette IDs under GMP. For regulated methods, follow ICH Q2(R1) precision requirements for the intended use.
Sterile compounding under USP General Chapter <797> requires aseptic technique, ISO-classified compounding environments, beyond-use dating, and independent verification of calculations for high-risk preparations. Diluent selection must preserve drug stability and sterility. Single-dose dilutions for patient administration require pharmacist verification and labeling that includes concentration, volume, and beyond-use date.
HPLC and LC-MS sample prep often dilutes stock or extracted solutions to bring analyte concentration within the validated calibration range and above the limit of quantitation (LOQ). Analysts calculate V1 from C1V1=C2V2 using the working standard concentration and target injection concentration, then dilute with matched matrix or mobile phase. Confirm diluted samples fall between LOD and LOQ using our LOD/LOQ Calculator when validating the method.

Related Calculators

SD Serial Dilution Calculator M Molarity Calculator LOD LOD/LOQ Calculator Prep Solution Preparation Conv Unit Converter

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