Solution Dilution Calculator
Plan your dilutions precisely ($C_1V_1 = C_2V_2$). Calculate required stock volume or final concentrations.
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Select a target variable and enter the known values to solve the dilution equation.
The Golden Rule of the Lab
Dilution is the art of turning a strong "Stock" solution into a usable "Working" solution. It is the single most common calculation performed in chemistry and biology labs worldwide.
The Dilution Equation
Before
High Concentration ($C_1$).
Small Volume ($V_1$).
After
Low Concentration ($C_2$).
Large Volume ($V_2$).
Safety First
The "AA" Rule
"Add Acid to water, like you ought-a."
Never pour water into a concentrated acid! The reaction is extremely exothermic (releases heat). The water can flash-boil instantly, spraying hot acid onto your skin. Always have a volume of water in the flask first, then slowly drip the acid in.
Serial Dilution
Sometimes you need to dilute something 1,000,000 times. Measuring 1 $\mu L$ into 1 Liter is inaccurate.
The Strategy:
- Take 1 mL sample + 9 mL water (1:10)
- Take 1 mL of that + 9 mL water (1:100)
- Take 1 mL of that + 9 mL water (1:1000)
Since $10 \times 10 \times 10 = 1000$, we achieved a massive dilution with easy-to-measure volumes.
Medicine (IV Drip)
Nurses dilute drugs constantly. A vial might contain 100mg/mL of a drug, but the patient needs a safe drip of 2mg/mL. An error here is fatal.
Biology Cultures
Microbiologists dilute bacteria samples to count colonies on a petri dish. If they don't dilute, the plate is just a solid lawn of bacteria—impossible to count.
Cooking Stocks
Chefs make "Stock" for a reason. Veal stock is reduced (concentrated) so it takes up less space in the fridge. When making soup, they dilute it back with water to normal strength.
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Frequently Asked Questions
What is the Dilution Equation?
The golden rule of the lab: $C_1V_1 = C_2V_2$. It states that the amount of solute in the start ($C_1 \times V_1$) equals the amount in the end ($C_2 \times V_2$). The only thing changing is the amount of water solvent.
Example: 10M to 1M dilution?
You have 10M stock. You want 500mL of 1M solution. $(10)(V_1) = (1)(500)$. $10V_1 = 500 \rightarrow V_1 = 50$ mL. So, take 50mL of stock and add 450mL of water.
Do I need to convert to Liters?
No! As long as $V_1$ and $V_2$ share the same unit (both mL or both L), the math works perfectly. This saves you from converting mL to L every time.
What is 'Serial Dilution'?
It's a stepwise dilution, often used in biology to count bacteria. Instead of diluting 1:1000 all at once (which is hard to measure), you dilute 1:10, then take that result and dilute 1:10 again, and again.
What is the Dilution Factor?
The Dilution Factor (DF) is the ratio of final volume to initial aliquot volume ($DF = V_2 / V_1$). If you mix 1 mL of sample with 9 mL of water (Total 10 mL), your DF is 10.
Why add Acid to Water? (Safety)
Remember: "Do as you oughta, add acid to wata." Mixing acid and water creates massive heat. A large volume of water can absorb this heat safely. A small puddle of acid will boil instantly if you add water to it, splashing corrosive liquid on your face.
Can I use this for Percent (%) solutions?
Yes. $C_1$ and $C_2$ can be any concentration unit: Molarity ($M$), Normality ($N$), mg/mL, or Percentage (%). Just keep them consistent.
How much solvent do I add?
The calculator gives you the Final Volume. To find how much pure solvent to add, subtract your starting volume: $V_{added} = V_2 - V_1$.
Does the number of moles change?
No. This is the core principle. You are just spreading the existing moles into a larger swimming pool. The number of particles remains constant.
What is a Stock Solution?
A highly concentrated solution kept in the lab to save space. Instead of storing 1000 bottles of 1M HCl, we store 1 bottle of 12M HCl and dilute it as needed.
Is volume always additive?
In general chemistry, yes ($50mL + 50mL = 100mL$). In strict analytical chemistry, no ($50mL$ Ethanol + $50mL$ Water < $100mL$ due to intermolecular packing). But for most dilute aqueous solutions, we assume additivity.
How do I make a 1:10 dilution?
Mix 1 part sample with 9 parts solvent. The total parts are $1+9=10$. This is a common confusion—people often mix 1 with 10 (making a 1:11 dilution).
What is an Aliquot?
An aliquot is the smaller volume of the initial sample ($V_1$) that you transfer into the new flask to be diluted.
Can I use density?
If you are diluting by mass (gravimetric dilution), yes. But this calculator is strictly volumetric ($C_1V_1$), which is standard for 99% of lab work.
Difference between M and m?
M (Molarity) is moles per L of solution (temperature dependent). m (Molality) is moles per kg of solvent (temperature independent). For dilute water solutions, they are roughly equal.