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The basics
Core Formula
Real-World Examples
Dilution Calculator – C₁V₁ = C₂V₂
Instantly find your stock volume or final volume — values update in real time as you type.
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The basics
How to Use This Dilution Calculator
This free dilution calculator works in two modes. Here’s how to get your answer in seconds:
- Choose your mode. Select Find Stock Volume (V₁) if you know your desired final volume and need to know how much stock to take. Select Find Final Volume (V₂) if you know how much stock you’re starting with.
- Enter C₁ — your stock or initial concentration (e.g., 1 M, 10%, 500 ppm).
- Enter C₂ — your desired final concentration (e.g., 0.1 M, 1%, 50 ppm).
- Enter the known volume — either V₂ (final volume) or V₁ (stock volume), depending on your mode.
- Select your units. Pick matching concentration and volume units from the dropdowns. Choose “Custom…” to type your own label.
- Read your results instantly. Tap “Show step-by-step” for the full working, or “Copy Results” to save your values.
Use the Reset button to return to defaults at any time. This solution dilution calculator recalculates automatically as you type — no submit button needed.
Core Formula
Understanding the Dilution Formula (C₁V₁ = C₂V₂)
The equation behind this C1V1 C2V2 calculator is one of the most fundamental in chemistry:
C₁V₁ = C₂V₂
Each variable represents:
- C₁ — the initial (stock) concentration of your solution.
- V₁ — the volume of stock solution you will take.
- C₂ — the desired final concentration after dilution.
- V₂ — the total final volume of the diluted solution.
The principle is simple: the amount of solute stays constant during dilution — you’re only adding more solvent. So C₁ × V₁ (moles in the stock portion) must equal C₂ × V₂ (moles in the final solution).
Rearranging for each unknown:
- To find V₁: V₁ = (C₂ × V₂) / C₁
- To find V₂: V₂ = (C₁ × V₁) / C₂
- To find C₁: C₁ = (C₂ × V₂) / V₁
- To find C₂: C₂ = (C₁ × V₁) / V₂
Units consistency is critical. C₁ and C₂ must be in the same units. V₁ and V₂ must share the same volume unit. This chemistry dilution calculator displays your chosen labels but does not convert between units — ensure your values are consistent before calculating.
Real-World Examples
Common Dilution Examples
💡 Making 1 L of 0.1 M NaCl from a 1 M stock
C₁ = 1 M, C₂ = 0.1 M, V₂ = 1000 mL
V₁ = (0.1 × 1000) / 1 = 100 mL of stock
Add 100 mL of 1 M stock to a volumetric flask, then top up to 1000 mL with distilled water.
V₁ = (0.1 × 1000) / 1 = 100 mL of stock
Add 100 mL of 1 M stock to a volumetric flask, then top up to 1000 mL with distilled water.
💡 Household bleach 1:10 dilution for disinfection
Bleach is typically 5% sodium hypochlorite. A 1:10 dilution gives 0.5%.
C₁ = 5%, C₂ = 0.5%, V₂ = 1000 mL
V₁ = (0.5 × 1000) / 5 = 100 mL of bleach + 900 mL water. A classic use case for a stock solution dilution calculator.
C₁ = 5%, C₂ = 0.5%, V₂ = 1000 mL
V₁ = (0.5 × 1000) / 5 = 100 mL of bleach + 900 mL water. A classic use case for a stock solution dilution calculator.
💡 Diluting a 10 mg/mL protein stock to 250 µg/mL
C₁ = 10,000 µg/mL, C₂ = 250 µg/mL, V₂ = 2000 µL
V₁ = (250 × 2000) / 10000 = 50 µL of stock + 1950 µL buffer. Common in ELISA and Western blot preparation.
V₁ = (250 × 2000) / 10000 = 50 µL of stock + 1950 µL buffer. Common in ELISA and Western blot preparation.
💡 Ethanol dilution from 95% to 70%
C₁ = 95%, C₂ = 70%, V₂ = 500 mL
V₁ = (70 × 500) / 95 ≈ 368.4 mL of 95% ethanol + 131.6 mL water.
Note: for precise alcohol dilution, a dedicated calculator applying density corrections accounts for volumetric contraction.
V₁ = (70 × 500) / 95 ≈ 368.4 mL of 95% ethanol + 131.6 mL water.
Note: for precise alcohol dilution, a dedicated calculator applying density corrections accounts for volumetric contraction.
Frequently Asked Questions
What is the dilution equation?
The standard dilution equation is C₁V₁ = C₂V₂, where C₁ is the initial concentration, V₁ is the volume of stock solution taken, C₂ is the desired final concentration, and V₂ is the total final volume. The equation holds because the total amount of solute (moles or mass) is conserved when you add solvent — only the volume changes. This dilution calculator applies this formula automatically in real time.
How do I calculate dilution factor?
The dilution factor (DF) is the ratio of the final volume to the stock volume used: DF = V₂ / V₁. Equivalently, DF = C₁ / C₂. For example, taking 10 mL of stock and diluting to 100 mL gives a dilution factor of 10, written as a 1:10 dilution. A dilution factor calculator simply divides C₁ by C₂. You can read V₁ and V₂ directly from this tool’s results.
Can I use different units for C₁ and C₂?
No — C₁ and C₂ must be in the same units for the formula to produce a correct result. If C₁ is in mol/L (M) and C₂ is in mmol/L, convert one before calculating. Similarly, V₁ and V₂ must share the same volume unit. This solution dilution calculator displays your selected unit labels but does not perform unit conversion. Mixing units will give an incorrect result.
What if my desired concentration is higher than my stock?
If C₂ > C₁, you cannot achieve the desired concentration by dilution — dilution only reduces concentration. You would need to use a more concentrated stock, evaporate solvent to concentrate your current solution, or prepare a fresh stock at a higher concentration. This calculator flags this scenario automatically with a warning message.
How does serial dilution work?
A serial dilution is a stepwise process where the output of one dilution step becomes the stock for the next. For example, a 1:10 serial dilution repeated three times gives concentrations of 1/10, 1/100, and 1/1000 of the original. Each individual step still follows C₁V₁ = C₂V₂. A serial dilution calculator chains multiple applications of this formula. You can use this tool for each step by entering the previous step’s output concentration as the new C₁.
Is this calculator accurate for alcohol dilution?
This liquid dilution calculator gives a mathematically correct answer using C₁V₁ = C₂V₂ for alcohol dilutions expressed as % v/v. However, mixing water and ethanol produces a slight volume contraction — the total volume is less than the sum of the two components. For most practical purposes the difference is small, but for precise applications such as commercial spirit blending or pharmaceutical ethanol preparation, a dedicated alcohol dilution calculator applying density tables and Gay-Lussac corrections is recommended. An advanced alcohol dilution calculator is coming soon!
Tips for Accurate Dilutions
- Always add solute to solvent — for concentrated acids especially, adding water to acid can cause dangerous exothermic reactions. Always add the concentrated solution into the bulk solvent.
- Use volumetric glassware — volumetric flasks, pipettes, and burettes are calibrated for precision. Use them over graduated cylinders for high-accuracy work.
- Mix thoroughly before measuring — incomplete mixing creates local concentration gradients that affect downstream measurements.
- Account for temperature — volumes change with temperature. Perform dilutions at the calibration temperature of your glassware (typically 20°C or 25°C) for critical work.
- Label everything immediately — include concentration, solvent, date, and your name on every container right after preparation.
- Double-check your units before entering values into any chemistry dilution calculator. Unit mismatches are the most common source of error.
Disclaimer: This dilution calculator is provided for educational and general laboratory reference purposes only. Results should be verified independently before use in regulated, clinical, food production, or safety-critical environments. Always consult relevant safety data sheets (SDS), standard operating procedures, and qualified professionals when working with hazardous chemicals. The tool assumes ideal mixing with no volume contraction and no unit conversion between C₁ and C₂ or between V₁ and V₂.
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