Mass per Volume Dilution Calculator and Formula

A mass-per-volume dilution calculator finds how much concentrated solution and diluent are needed to make a target volume at a lower concentration. Enter the stock concentration, desired concentration, and final volume; the calculator returns the stock volume to measure and the diluent volume to add.

Formula

The standard dilution relationship is C₁V₁ = C₂V₂. Solving for the volume of stock solution gives V₁ = C₂V₂ / C₁. The calculator uses the same concentration unit for both concentrations and the same volume unit for both volumes.

• C₁ is the starting, or stock, concentration in grams per liter (g/L).
• V₁ is the volume of stock solution to use, in milliliters (mL).
• C₂ is the desired final concentration in g/L.
• V₂ is the total final solution volume in mL.

The diluent volume shown is V₂ − V₁. It is the amount to add when preparing the mixture by combining measured stock with diluent. The equation assumes the solute amount stays the same during dilution and that volumes are additive for the intended calculation.

Worked Example

Using the calculator’s default values, the stock concentration is 100 g/L, the target concentration is 10 g/L, and the final volume is 100 mL.

1. Apply the dilution equation: V₁ = C₂V₂ / C₁.
2. Substitute the values: V₁ = (10 g/L × 100 mL) / 100 g/L.
3. Cancel the matching concentration units: V₁ = 10 mL of stock solution.
4. Find the diluent volume: 100 mL − 10 mL = 90 mL.

So the calculator returns 10.00 mL of stock solution and 90.00 mL of diluent. In practice, if the final volume must be exact, a common preparation approach is to add stock and then bring the mixture up to the final volume with diluent, rather than assuming separately measured volumes always combine to precisely that total.

What Mass per Volume Means

A mass-per-volume concentration describes the mass of a substance in a specified volume of solution. For example, 10 g/L means 10 grams of solute per liter of solution. Other common expressions include milligrams per milliliter (mg/mL), grams per 100 milliliters (g/100 mL), and percent weight/volume (% w/v). In the usual % w/v convention, 1% means 1 gram per 100 mL of final solution.

Mass per volume is not the same as mass fraction or volume percent. A value such as 10% w/v gives a mass of solute per volume of solution; 10% w/w instead means a mass of solute per mass of mixture. Do not enter values from these different concentration types as though their units were interchangeable.

How to Use the Result

First check that the stock is more concentrated than the target. Then measure the calculated stock volume and prepare the chosen final volume. The result is a mathematical quantity, not a direction to use any particular chemical or material; follow the relevant product instructions and laboratory procedures for handling and preparation.

• Stock solution needed is the portion of concentrated solution that supplies the solute.
• Diluent to add is the difference between the target final volume and the stock volume.
• Final volume means the total amount of solution after dilution, not the amount of diluent alone.

For a larger batch, scale the final volume while keeping the desired concentration fixed. For example, doubling the final volume also doubles the stock volume required, provided the stock concentration and target concentration stay unchanged.

Units, Accuracy, and Common Mistakes

The calculator accepts g/L for both concentration inputs and mL for both volume values. Other units can be used with the same equation, but convert them consistently first. For instance, 1 g/L equals 1 mg/mL, while 1 L equals 1,000 mL. A US customary volume such as a fluid ounce must also be converted before combining it with milliliters; a fluid ounce measures volume, not mass.

• Mixing concentration units: Convert stock and target concentrations to the same unit before using the ratio.
• Confusing final volume with diluent: The desired volume is the total mixture volume. Do not add that full amount of diluent on top of the stock.
• Rounding too early: Keep extra digits during intermediate calculations and round only the measured result to match the precision of the available equipment.
• Using a weaker stock: If the target concentration exceeds the stock concentration, ordinary dilution cannot produce it. A more concentrated source or a different preparation method is required.
• Assuming exact volume additivity: Some mixtures can change volume when combined. When exact concentration matters, prepare to a defined final volume using an appropriate calibrated vessel and procedure.

Limits and Related Dilution Calculations

This calculator handles a single dilution from one stock solution to one target solution. It does not account for solute loss, chemical reactions, evaporation, density changes, purity, or measurement uncertainty. Those factors can matter in specialized preparations, so the simple equation should not replace a validated procedure where one is required.

For serial dilution, the output of one step becomes the stock for the next. Calculate each step separately, keeping track of the concentration after every dilution. The overall concentration factor is the product of the individual dilution factors; for example, two successive tenfold dilutions result in a hundredfold dilution relative to the original stock.

Frequently Asked Questions

How do I calculate a mass-per-volume dilution?
Use C₁V₁ = C₂V₂. Rearrange it to V₁ = C₂V₂ / C₁ to find the stock volume, then subtract that volume from the desired final volume to estimate the diluent amount.

What is the difference between mass per volume and percent w/v?
They describe the same general type of concentration but use different units. Percent w/v conventionally states grams of solute per 100 mL of final solution; convert it to a matching unit such as g/L before comparing it with another concentration.

Do I add the diluent volume or fill to the final volume?
The calculator’s diluent figure is the difference between final and stock volumes. If an exact final volume is needed, a preparation procedure may instead call for adding diluent until the total reaches the stated final volume.

Can I dilute a solution to a higher concentration?
No. Adding diluent lowers concentration. A target above the stock concentration requires a more concentrated stock or another preparation approach.

Can I use different units for the two concentrations?
Not directly in the equation. Convert both concentrations to the same mass-per-volume unit, and make sure the stock and final volume values use compatible volume units.

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in stock | Stock concentration | g/L | 100 | 0
in target | Target concentration | g/L | 10 | 0
in final | Final volume | mL | 100 | 0
out stockvol | Stock solution needed | mL | target * final / stock | 2
out diluent | Diluent to add | mL | final - stockvol | 2