Goal
Use C₁V₁ = C₂V₂ to check an entered stock volume, calculate the stock volume needed for a target concentration, and find the diluent volume.
Solution Dilution Calculator
Use C₁V₁ = C₂V₂ to check an entered stock volume, calculate the stock volume needed for a target concentration, and find the diluent volume.
Key facts
- What it does
- Use C₁V₁ = C₂V₂ to check an entered stock volume, calculate the stock volume needed for a target concentration, and find the diluent volume.
- Formula
C₁V₁ = C₂V₂; required stock volume = C₂V₂ ÷ C₁; diluent volume = final volume − required stock volume; actual concentration from the entered stock volume = C₁V₁ ÷ V₂.- You enter
- Stock concentration · Entered stock volume · Target concentration · Final solution volume
- Worked example
- The required stock volume is 0.1 L and the diluent volume is 0.9 L. The entered stock volume produces 0.5 mol/L in the 1 L final-volume scenario.
A clearer path to an answer
From your question to a useful result
This page keeps the calculation transparent: define the goal, enter the matching values, inspect the method, and decide what the result means in your situation.
Inputs
Stock concentration · Entered stock volume · Target concentration · Final solution volume
Method
C₁V₁ = C₂V₂; required stock volume = C₂V₂ ÷ C₁; diluent volume = final volume − required stock volume; actual concentration from the entered stock volume = C₁V₁ ÷ V₂.
Next step
Calculate, review the assumptions below, then compare a related tool when the decision needs more context.
Solution Dilution Calculator
Use C₁V₁ = C₂V₂ to check an entered stock volume, calculate the stock volume needed for a target concentration, and find the diluent volume.
Open the Solution Dilution Calculator pageMore science tools
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Result
Enter your values above and choose Calculate to see the result here.
Calculation map
Follow the path from input to answer
01
Inputs (4)
- Stock concentration Ready
- Entered stock volume Ready
- Target concentration Ready
- Final solution volume Ready
02
Formula
C₁V₁ = C₂V₂; required stock volume = C₂V₂ ÷ C₁; diluent volume = final volume − required stock volume; actual concentration from the entered stock volume = C₁V₁ ÷ V₂.
Bounded, transparent calculation
03
Result
- Calculate to preview the result.
Recent runs
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Formula, assumptions, and example
Formula: C₁V₁ = C₂V₂; required stock volume = C₂V₂ ÷ C₁; diluent volume = final volume − required stock volume; actual concentration from the entered stock volume = C₁V₁ ÷ V₂.
This worksheet distinguishes the stock volume actually entered from the stock volume required to hit the target. That comparison makes it easier to catch a preparation that has the right stock concentration but the wrong pipetted volume.
- The stock and target concentrations use the same concentration unit and the two volumes use the same volume unit.
- The target concentration does not exceed the stock concentration because the operation is dilution by adding solvent or diluent.
- The final volume is treated as the completed solution volume, not simply an uncorrected sum of raw liquid volumes.
- The solute amount is conserved during ideal dilution and no reaction, precipitation, evaporation, or adsorption occurs.
- Density, purity, temperature, volumetric-flask tolerance, and mixing procedure are outside the equation.
- A concentration calculation does not approve a chemical procedure or determine safe handling.
- Use the material's actual concentration definition when it is not molarity, and keep units consistent.
Worked example: The required stock volume is 0.1 L and the diluent volume is 0.9 L. The entered stock volume produces 0.5 mol/L in the 1 L final-volume scenario.
Displayed input contract
- Stock concentration · minimum 1.0E-9 · maximum 1000000000
- Entered stock volume · minimum 1.0E-6 · maximum 1000000000
- Target concentration · minimum 1.0E-9 · maximum 1000000000
- Final solution volume · minimum 1.0E-6 · maximum 1000000000
The displayed limits are checked before the handler runs. Model-specific domain checks may also reject impossible or non-finite inputs.
Methodology: This calculator follows the WorldCalculate input, formula, precision, and boundary policy. Read the official methodology.
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Answer-first guide
How to use the Solution Dilution Calculator for a real question
Use C₁V₁ = C₂V₂ to check an entered stock volume, calculate the stock volume needed for a target concentration, and find the diluent volume. Start with one clearly defined goal, enter values in the units shown, and keep the result attached to the assumptions below.
What this answers
This tool is useful when your question includes solution dilution calculator, C1V1 C2V2 calculator, molar dilution calculator. It returns the outputs declared in the calculator contract rather than a live quote, approval, diagnosis, or professional sign-off.
What you enter
Stock concentration · Entered stock volume · Target concentration · Final solution volume. Keep the same time period, unit system, and currency wherever the form requires comparable values.
How to check it
Run the worked example first, compare its output with the page's example, then change one input at a time. This makes an unexpected result easier to trace to a unit, boundary, or assumption.
Three checks before you rely on the answer
- Match the question. Confirm that the result means the quantity you need, not a similar-sounding percentage, balance, rate, or estimate.
- Match the inputs. Use the requested units and period, and read each hint before replacing the example values with your own.
- Read the boundary. Review the assumptions and limits. The stock and target concentrations use the same concentration unit and the two volumes use the same volume unit.
Need a wider view? Browse Science Calculators or compare the related tools below. The WorldCalculate methodology explains how formulas, examples, limits, and revisions are reviewed.
How to use the Solution Dilution Calculator
- Enter Stock concentration (mol/L).
- Enter Entered stock volume (L).
- Enter Target concentration (mol/L).
- Enter Final solution volume (L).
- Choose Calculate and read the result panel.
- Use Download PDF or Download Word to save a result sheet.
Formula
C₁V₁ = C₂V₂; required stock volume = C₂V₂ ÷ C₁; diluent volume = final volume − required stock volume; actual concentration from the entered stock volume = C₁V₁ ÷ V₂.
This worksheet distinguishes the stock volume actually entered from the stock volume required to hit the target. That comparison makes it easier to catch a preparation that has the right stock concentration but the wrong pipetted volume.
Worked example
The required stock volume is 0.1 L and the diluent volume is 0.9 L. The entered stock volume produces 0.5 mol/L in the 1 L final-volume scenario.
Assumptions and limits
- The stock and target concentrations use the same concentration unit and the two volumes use the same volume unit.
- The target concentration does not exceed the stock concentration because the operation is dilution by adding solvent or diluent.
- The final volume is treated as the completed solution volume, not simply an uncorrected sum of raw liquid volumes.
- The solute amount is conserved during ideal dilution and no reaction, precipitation, evaporation, or adsorption occurs.
- Density, purity, temperature, volumetric-flask tolerance, and mixing procedure are outside the equation.
- A concentration calculation does not approve a chemical procedure or determine safe handling.
- Use the material's actual concentration definition when it is not molarity, and keep units consistent.
Who uses this calculator?
- Chemistry students practicing dilution equations
- Laboratory learners checking a stock preparation
- Teachers demonstrating conservation of solute amount
When is it useful?
- Dilute a 5 mol/L stock to 0.5 mol/L in a 1 L final solution.
- Compare the entered stock volume with the required volume.
- Calculate how much diluent remains after the target stock volume is selected.
Context and background
The model-first approach to science
Science calculators define a system, choose an equation, apply units and constants, and show the substitution. Effects outside that model remain outside the result.
Introductory science problem solving builds from measured quantities and idealized relationships. Those models are valuable for learning and first-pass estimates, while experiments and engineering decisions need additional evidence.
Research and review
How this guide was researched
Researched by Hassan ALRowaie, Founder and editorial researcher at WorldCalculate.
This guide follows the live calculator's declared inputs, formula, worked example, assumptions, validation boundaries, and source-backed methodology. The review date describes editorial review of the calculator explanation; it is not a promise that external facts or rates remain current.
Dilution is often taught as C₁V₁ = C₂V₂, but a practical worksheet also needs to show which volume is being planned and which volume was actually entered. This calculator reports both paths so the concentration check can be audited.
What a dilution preserves
In an ideal dilution, the amount of solute is unchanged while the solution volume increases. Concentration falls because the same solute amount occupies a larger final volume.
The conservation statement is C₁V₁ = C₂V₂ when concentration and volume units are compatible.
The stock-volume calculation
To prepare a target concentration C₂ in a final volume V₂ from stock concentration C₁, rearrange the equation to V₁ = C₂V₂/C₁.
The calculator reports this required stock volume separately from the entered stock volume. If they differ, the entered preparation will not reach the requested target under the ideal model.
Worked example
For a 5 mol/L stock, target 0.5 mol/L, and final volume 1 L, the required stock volume is 0.5 × 1 ÷ 5 = 0.1 L.
The remaining final-volume difference is 1 − 0.1 = 0.9 L of diluent in the scenario. The result describes volume arithmetic, not a laboratory instruction for a particular chemical.
Checking an entered stock volume
The same page calculates the concentration produced by the stock volume actually entered: C = C₁V₁/V₂. This is useful when a pipette or measuring cylinder has already been selected.
A mismatch between actual and required stock volume is evidence to review the setup, units, final-volume definition, or target before proceeding.
Units must travel together
Molarity in mol/L pairs naturally with litres, but any compatible concentration and volume units can work if they cancel consistently. Do not mix millilitres with litres without a conversion.
The equation does not convert mass concentration to molarity. That requires molar mass and, when relevant, density or a material-specific concentration definition.
Why final volume is not always an addition
The calculator treats final volume as the completed solution volume. In real mixtures, volumes may not add perfectly because of contraction, temperature, or material properties.
Use an appropriate volumetric procedure and a validated protocol when the final concentration matters. The simple equation remains a valuable check of the intended quantities.
Safety and professional boundaries
A correct dilution number does not establish compatibility, toxicity, sterility, temperature control, labeling, or safe disposal. Those decisions depend on the material and setting.
Follow institutional procedures, product instructions, and qualified supervision. Keep the calculator result as a transparent arithmetic record rather than a substitute for procedure.
FAQs
What if the target is higher than the stock? That is not a dilution; the handler rejects it. Why does the page ask for stock volume and target volume? The entered volume lets you check an actual plan while the target volume lets you solve the ideal required volume. Can the equation use percent concentration? Yes, if both concentrations use the same defined basis, but do not mix w/v with w/w.
Frequently asked questions
What is the Solution Dilution Calculator?
Use C₁V₁ = C₂V₂ to check an entered stock volume, calculate the stock volume needed for a target concentration, and find the diluent volume.
What is the formula for the Solution Dilution Calculator?
C₁V₁ = C₂V₂; required stock volume = C₂V₂ ÷ C₁; diluent volume = final volume − required stock volume; actual concentration from the entered stock volume = C₁V₁ ÷ V₂. This worksheet distinguishes the stock volume actually entered from the stock volume required to hit the target. That comparison makes it easier to catch a preparation that has the right stock concentration but the wrong pipetted volume.
What do I need to use this calculator?
Enter Stock concentration, Entered stock volume, Target concentration, Final solution volume, then choose Calculate.
What are the limits of this calculator?
The stock and target concentrations use the same concentration unit and the two volumes use the same volume unit. The target concentration does not exceed the stock concentration because the operation is dilution by adding solvent or diluent. The final volume is treated as the completed solution volume, not simply an uncorrected sum of raw liquid volumes. The solute amount is conserved during ideal dilution and no reaction, precipitation, evaporation, or adsorption occurs. Density, purity, temperature, volumetric-flask tolerance, and mixing procedure are outside the equation. A concentration calculation does not approve a chemical procedure or determine safe handling. Use the material's actual concentration definition when it is not molarity, and keep units consistent.
Methodology
This calculator is part of the WorldCalculate library. Its formula, example, assumptions, input bounds, and output formatting follow the official methodology.
Use this calculator as part of a bigger plan
These WorldCalculate collections connect this tool with related questions while keeping each calculation separate and transparent.