Dilution Calculator for C1V1 = C2V2
Dilution Calculator for C1V1 = C2V2: solve stock volume, final concentration, final volume, dilution factor, and 1:2 or 1:10 lab dilutions.
A simple dilution is a one-step preparation where you take a measured amount of stock solution and add enough diluent to reach a lower concentration. The stock might be a bottle of concentrated reagent, a buffer made earlier in the week, a teaching-lab sample, or a standard supplied by another method. The diluent is usually water, buffer, or the same solvent system listed in the protocol. The amount of solute does not change during the dilution. Only the total volume changes.
This calculator is meant for the ordinary lab question: "How much of the stock do I need, and what final volume will I have?" It handles the common C1V1 = C2V2 setup, ratio dilutions such as 1:2 or 1:10, serial dilution planning, and concentration unit conversion. For a quick 1:2 dilution, one part stock is present in two total parts. That is usually made by mixing equal volumes of stock and diluent. If the stock is 20 mM, the 1:2 dilution is 10 mM after mixing.
Simple dilution works best when the required stock volume is easy to measure and the final solution behaves normally after mixing. If the calculation asks for 2.5 mL of stock and 47.5 mL of buffer, the bench work is straightforward. If it asks for 0.37 microliters of stock, the arithmetic may be correct, but the preparation is not practical with normal classroom or benchtop equipment. In that case, prepare an intermediate dilution or switch to a serial dilution plan.
C1V1 = C2V2 says that the amount of solute before dilution equals the amount of solute after dilution. C1 is the concentration of the stock solution. V1 is the stock volume transferred. C2 is the target or final concentration. V2 is the total final volume after diluent has been added. The equation is a mass balance written in concentration and volume terms.
Use the C1V1 = C2V2 calculator when you want the equation by itself with a focused formula table. Use this dilution calculator when you also want ratio dilution, serial dilution, and concentration conversion support on the same page. Both tools use the same conservation idea: the stock portion carries a fixed amount of solute into a larger final volume.
| Unknown | Rearranged equation | Use it when |
|---|---|---|
| C1 | C1 = (C2 × V2) ÷ V1 | You need the stock strength required. |
| V1 | V1 = (C2 × V2) ÷ C1 | You need the stock volume to pipette. |
| C2 | C2 = (C1 × V1) ÷ V2 | You need the final concentration. |
| V2 | V2 = (C1 × V1) ÷ C2 | You need the final volume to make. |
Here is the classroom version of the calculation. Suppose the stock is 2.0 M, the target is 0.50 M, and the final volume needs to be 100 mL. Solve V1 = (C2 × V2) ÷ C1. Substitution gives V1 = (0.50 M × 100 mL) ÷ 2.0 M = 25 mL. Transfer 25 mL of the stock solution, then add diluent until the total volume is 100 mL. The amount of diluent is not 100 mL. It is 75 mL because the stock volume is already part of the final solution.
A stock solution is a concentrated solution prepared so smaller, lower-concentration working solutions can be made from it later. Labs use stock solutions because they save space, reduce repeated weighing, and keep day-to-day preparations more consistent. A 1.0 M stock can be diluted to 0.10 M, 10 mM, or another working concentration as long as the units are converted before the calculation.
Stock dilution planning starts with the target solution, not with the bottle. Write down the final concentration you need, the final volume required by the lab, and the solvent or buffer that should make up the rest of the volume. Then solve for V1, the stock volume. If V1 falls outside a good pipetting range, change the final volume or make an intermediate stock. The calculator can show the arithmetic, but the glassware still decides whether the plan is sensible.
Labels matter with stock solutions. A bottle marked "10x" is not the same as a bottle marked "10 mM." A percent stock may mean percent weight/volume, percent volume/volume, or percent weight/weight. A molar stock may need a molar mass calculation upstream if you are preparing it from solid reagent. When that is the part you are solving, the molarity and molar mass calculators are a better starting point.
Final concentration is the concentration after the stock and diluent have been mixed to the final volume. Solve for C2 when you already know how much stock was used and what total volume was made. This is useful for checking a preparation after the fact, reviewing a lab notebook entry, or teaching why adding more solvent lowers concentration.
The rearranged equation is C2 = (C1 × V1) ÷ V2. If 5 mL of a 4.0 M stock is diluted to 100 mL total volume, C2 = (4.0 M × 5 mL) ÷ 100 mL = 0.20 M. The same relationship works for mg/mL, percent weight per volume, ppm, cells per mL, or another concentration label as long as the unit is used consistently on both sides.
Final concentration is not the same as product amount or reaction recovery. If you are checking how much product a reaction made, use a yield calculation instead of a dilution calculation. The percent yield calculator belongs to that part of the workflow. Dilution answers the solution concentration question after a known amount of solute has been spread through a known volume.
The calculator also reports dilution factor and stock fraction. Those two values help you read the result without repeating the whole equation. A dilution factor of 20x means the final concentration is one twentieth of the stock concentration. A stock fraction of 5% means the stock solution makes up five percent of the final volume.
"Volume needed" can mean two different things in a dilution problem. Most of the time, it means the stock volume to transfer, which is V1. If you know the stock concentration, target concentration, and desired final volume, solve V1 = (C2 × V2) ÷ C1. The calculator then shows the stock volume and the amount of diluent to add.
Sometimes volume needed means the final volume you can make from a fixed amount of stock. In that case, solve V2 = (C1 × V1) ÷ C2. This setup comes up when a student has only a limited amount of stock solution left, or when a lab wants to know how far a reagent aliquot can be diluted to reach a target working concentration.
Be careful with diluent volume. If the final volume is 50 mL and the stock volume is 5 mL, you add 45 mL of diluent, not 50 mL. In a volumetric flask, transfer the stock first, add some diluent and mix, then bring the liquid level to the mark. In a tube or beaker, use the same idea with the best volume marks and pipettes available for the job.
Dilution does not identify the solute or calculate its formula mass. If you are turning grams of a compound into moles before making a stock solution, you may need molar mass data first. Some students also meet average atomic mass in the same sequence of topics; the average atomic mass calculator is useful there, but it is separate from the dilution step itself.
A simple dilution uses one transfer from the stock solution. A serial dilution uses repeated transfers, where each new tube is made from the previous tube. Use a serial dilution when the target concentration is far below the stock, when you need a set of standards, or when a single direct dilution would call for a stock volume that is too small to measure well.
For example, a 1:1000 dilution can be made in one step only if the stock and final volumes are practical. Transferring 1 microliter into 999 microliters may be possible with the right pipette, but it leaves little room for technique error. Three 1:10 steps are often easier to handle: 100 microliters into 900 microliters, mix, then repeat twice. The total dilution is still 1:1000 because the factors multiply.
The serial dilution calculator is built for that tube-by-tube planning. It shows the concentration after each step and the cumulative dilution factor. This dilution calculator includes a serial mode for quick checks, but the dedicated page is easier to use when the whole task is a dilution series.
Serial dilution is not automatically more accurate. Every transfer and every mixing step can add error. Use it when it makes the transfers measurable or when the method calls for a concentration series. If a single dilution has a clean pipetting volume and the lab only needs one final solution, the simple C1V1 = C2V2 calculation is usually the better choice.
Most dilution errors are unit errors or volume-definition errors. C1 and C2 must use the same concentration unit before you apply the equation. V1 and V2 must use the same volume unit. If the stock is in M and the target is in mM, convert one of them first. If the transfer volume is in microliters and the final volume is in milliliters, convert before calculating or use a calculator mode that keeps the labels consistent.
Percent solutions need a little extra care. A 5% w/v solution means 5 g per 100 mL final solution. A 5% v/v solution means 5 mL solute per 100 mL final solution. A 5% w/w solution is based on mass, not volume. The dilution equation can handle percent values when the percent type is the same on both sides, but it cannot guess density or composition from the percent sign alone.
A good dilution record is short but specific. Write the stock concentration, target concentration, final volume, equation used, and calculated stock volume before you pick up a pipette. If the stock came from a bottle, copy the label information. If it came from a previous preparation, copy the notebook page or batch name. This is the boring part of dilution work, but it saves a lot of guessing when a result does not look right later.
After the calculation, choose glassware that fits the answer. A volumetric flask is best when the final volume must be accurate. A graduated cylinder or conical tube may be fine for rough teaching-lab work. A micropipette is only as good as its range, tip fit, and user technique. If the calculated stock volume sits near the bottom of a pipette range, use a larger preparation or an intermediate dilution so the transfer is easier to make cleanly.
Add the measured stock to the container, add part of the diluent, and mix. Then bring the solution to the final volume and mix again. This order keeps the solution closer to uniform while you finish the preparation. For buffered, biological, volatile, or hazardous solutions, follow the lab protocol for temperature, order of addition, storage, and personal protective equipment. The calculator checks the math; it does not replace the method.
Label the prepared solution as soon as it is made. A useful label includes final concentration, solvent or buffer, date, preparer, and any storage condition that matters. If the solution will be used for an assay or a report, keep the formula substitution with the record. The calculator breakdown is written in that style so it can be copied into a notebook without turning the entry into a mystery later.
When the result is part of a larger chemistry problem, keep each tool in its lane. Use molarity or molar mass calculations to prepare the stock, this dilution calculator to plan the working solution, the serial dilution calculator for concentration series, and yield tools for reaction recovery. That separation makes the work easier to check because each number has a clear job.
Enter any three values from C1, V1, C2, and V2, then solve for the missing one. C1 and V1 describe the stock solution you start with. C2 and V2 describe the final solution after adding diluent. Keep both concentration values in the same unit and both volume values in the same unit.
A 1:2 dilution means one part stock in two total parts. In the lab, that is usually made by mixing equal volumes of stock and diluent, such as 1 mL stock plus 1 mL water or buffer. The final concentration is half of the stock concentration.
Dilution factor tells how many times more dilute the final solution is than the stock solution. For a standard dilution, dilution factor = C1/C2 = V2/V1. A 10x dilution gives a final concentration that is one tenth of the stock concentration.
Use a serial dilution when a single dilution would require a transfer volume that is too small to pipette well, when you need several related standards, or when the target concentration is many orders of magnitude below the stock. A serial dilution reduces the concentration in repeated steps, such as 1:10, then 1:100, then 1:1000.
Yes. C1 and C2 must use the same concentration unit, and V1 and V2 must use the same volume unit before the equation is applied. Convert mM to M, microliters to milliliters, or mg/mL to µg/mL first. Do not mix molarity with mass concentration unless you also know the molar mass and perform the conversion.
The most common mistakes are adding diluent volume instead of bringing the solution to final volume, treating a 1:10 dilution as one part stock plus ten parts diluent, mixing units, using an old stock concentration, skipping mixing, and reporting more decimals than the glassware can support.
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