⭐ Starlight Tools / Dilution Calculator

Understanding the Dilution Formula (C1V1 = C2V2)

The dilution equation $C_1V_1 = C_2V_2$ is a fundamental formula used in chemistry and biology to calculate the parameters of a solution before and after dilution. It's based on the principle that the **amount of solute remains constant** during a dilution process.

Components of the Formula:

• $C_1$: **Initial Concentration** (the concentration of the stock solution).
• $V_1$: **Initial Volume** (the volume of the stock solution you will use).
• $C_2$: **Desired Final Concentration** (the concentration of the diluted solution you want to prepare).
• $V_2$: **Desired Final Volume** (the total volume of the diluted solution you want to prepare).

How it Works:

When you dilute a solution, you add more solvent (e.g., water) to it, which increases the total volume and decreases the concentration of the solute. However, the actual amount (moles or mass) of the solute itself does not change. The formula $C_1V_1$ represents the amount of solute in the initial solution, and $C_2V_2$ represents the amount of solute in the final (diluted) solution. Since these amounts are equal, we can set the two expressions equal to each other.

Common Use Cases:

1. **Calculating Unknown Final Volume ($V_2$):** If you know your stock concentration ($C_1$), the volume of stock you're using ($V_1$), and your desired final concentration ($C_2$), you can calculate how much total volume ($V_2$) your diluted solution will be. This is useful for determining how much solvent to add.
   Formula: $V_2 = (C_1 \times V_1) / C_2$
2. **Calculating Unknown Initial Volume ($V_1$):** If you know your stock concentration ($C_1$), your desired final concentration ($C_2$), and your desired final volume ($V_2$), you can calculate how much of the stock solution ($V_1$) you need to start with. This is perhaps the most common application in a lab.
   Formula: $V_1 = (C_2 \times V_2) / C_1$
3. **Calculating Unknown Final Concentration ($C_2$):** If you know your stock concentration ($C_1$), the initial volume you took ($V_1$), and the total final volume after dilution ($V_2$), you can calculate the resulting concentration ($C_2$) of your new solution.
   Formula: $C_2 = (C_1 \times V_1) / V_2$
4. **Calculating Unknown Initial Concentration ($C_1$):** Less common, but if you know the diluted solution's concentration ($C_2$) and volume ($V_2$), and the volume of the original stock used ($V_1$), you can find the original stock concentration ($C_1$).
   Formula: $C_1 = (C_2 \times V_2) / V_1$

Important Note on Units: For the calculation to be correct, the units for concentration (C1 and C2) must be the same, and the units for volume (V1 and V2) must be the same. The calculator does not convert units; it assumes consistency. For example, if $C_1$ is in Molarity (M), $C_2$ will be in Molarity (M). If $V_1$ is in milliliters (mL), $V_2$ will be in milliliters (mL).

How This Tool Works

This Dilution Calculator operates entirely client-side within your browser. No data is sent to a server, ensuring your privacy. It takes the values you input, identifies which one is left blank, and then uses the $C_1V_1 = C_2V_2$ formula to solve for the missing variable. It performs basic mathematical operations to provide the result instantly.