Solute volume equals desired strength percentage divided by stock strength percentage times desired quantity
Solution
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Worked Examples
Use these nursing scenarios to sanity-check the formula, then load the same values back into the calculator with one click.
Basic Dilution
How do you make 1000 mL of 25% solution from 50% stock?
This is the classic half-strength-from-double-strength dilution problem.
Set Desired % = 25, Stock % = 50, and Total Volume = 1000 mL.
Use the formula Solute = (Desired % / Stock %) × Total Volume.
Substitute the values: Solute = (25 / 50) × 1000.
Solve the ratio: 25 / 50 = 0.5.
Multiply by total volume: 0.5 × 1000 = 500 mL of stock solution.
Subtract from the total volume: 1000 - 500 = 500 mL of diluent.
A 25% target is exactly half the 50% stock, so the stock and diluent end up equal here.
Smaller Batch
How do you make 250 mL of 10% solution from 40% stock?
This example shows a lower target concentration and a smaller final batch size.
Set Desired % = 10, Stock % = 40, and Total Volume = 250 mL.
Use Solute = (Desired % / Stock %) × Total Volume.
Substitute the values: Solute = (10 / 40) × 250.
Solve the ratio: 10 / 40 = 0.25.
Multiply by total volume: 0.25 × 250 = 62.5 mL of stock solution.
Subtract from the final batch size: 250 - 62.5 = 187.5 mL of diluent.
This pattern is common when preparing a small-volume bedside or treatment-room solution.
Near-Stock Strength
How do you make 500 mL of 45% solution from 60% stock?
When the desired concentration is close to the stock concentration, most of the final mixture will be stock solution.
Set Desired % = 45, Stock % = 60, and Total Volume = 500 mL.
Use Solute = (Desired % / Stock %) × Total Volume.
Substitute the values: Solute = (45 / 60) × 500.
Solve the ratio: 45 / 60 = 0.75.
Multiply by total volume: 0.75 × 500 = 375 mL of stock solution.
Subtract from the final total: 500 - 375 = 125 mL of diluent.
A result like this is a good reminder that solvent volume shrinks as the target concentration approaches the stock strength.
Solution Reconstitution Formula
Calculates how much concentrated stock solution (solute) and how much diluent (solvent) to combine to prepare a solution at the desired concentration and volume.
Enter the desired solution strength (%), the stock solution strength (%), and the total volume needed. The calculator determines the solute volume (stock solution) and the solvent volume (diluent) required to produce the final solution at the desired concentration.
Example Problem
Prepare 1,000 mL of a 25% solution from a 50% stock solution.
Identify the target concentration: 25%.
Identify the stock concentration: 50%.
Identify the final total volume needed: 1000 mL.
Apply the formula Solute = (Desired % / Stock %) × Total Volume = (25 / 50) × 1000.
Solve the equation: 25 ÷ 50 = 0.5, then 0.5 × 1000 = 500 mL of stock solution.
Subtract solute from the final total volume: 1000 - 500 = 500 mL of solvent.
The desired strength can never exceed the stock strength — you cannot concentrate a solution by adding diluent.
Key Concepts
Solution reconstitution is the process of diluting a concentrated stock solution to a lower, desired concentration. This is commonly needed for enteral feedings, oral rehydration solutions, topical antiseptics, and irrigation solutions. Always verify the appropriate diluent from the manufacturer's package insert.
Applications
Diluting concentrated enteral feeding formulas
Preparing oral rehydration solutions at specific concentrations
Setting the desired strength higher than the stock strength (impossible by dilution alone)
Using the wrong diluent (always check the package insert)
Confusing solute volume with total volume
Not labeling the prepared solution with concentration, date, and expiration
Frequently Asked Questions
What is the difference between solute and solvent?
The solute is the substance being dissolved (the concentrated stock solution). The solvent is the liquid used to dilute it (such as sterile water or normal saline). Together they make up the final desired solution.
Can the desired strength exceed the stock strength?
No. You cannot make a solution stronger than the stock solution by dilution alone. The desired strength percentage must be equal to or less than the stock strength. If a higher concentration is needed, a different stock solution must be used.
What diluent should I use for reconstitution?
The appropriate diluent depends on the medication and its intended use. Common diluents include sterile water for injection, normal saline (0.9% NaCl), and bacteriostatic water. Always check the drug manufacturer's package insert for the recommended diluent, as using the wrong one can cause precipitation, reduced potency, or patient harm.
What is the formula for solution reconstitution?
A simple bedside dilution setup is Solute Volume = (Desired Strength ÷ Stock Strength) × Total Final Volume. Once you know the solute volume, subtract it from the desired final volume to find the amount of solvent needed.
Why does the final solvent volume matter just as much as the solute volume?
Because the total final batch depends on both parts. You are not only calculating how much stock solution to use, you are also ensuring the combined solute and solvent volumes produce the final ordered concentration and total volume.
When should a reconstitution calculation be double-checked?
Always double-check when the final batch is large, when the stock is a high-alert medication, when the diluent must be product-specific, or when the target concentration is close to the stock concentration. Those situations magnify the impact of a simple arithmetic or labeling mistake.
Reference:
United States Pharmacopeia (USP) compounding guidance and manufacturer package-insert dilution instructions for stock-solution preparation and reconstitution.
Disclaimer: This calculator is intended for educational purposes and to assist with solution preparation calculations. All results should be independently verified by a qualified healthcare professional. Always follow your facility's policies.