What this calculator does
The standard dilution equation is \(C_1 \cdot V_1 = C_2 \cdot V_2\), where C1 and V1 are the concentration and volume of the original (stock) solution, and C2 and V2 are the concentration and volume of the final diluted solution. This tool rearranges the equation to solve for the original concentration C1 when you know the final concentration, the final volume, and the volume of stock that was used.
How to use it
Enter the final concentration (C2), the final volume (V2), and the initial volume of stock taken (V1). Keep your concentration units consistent (M, mg/mL, %, etc.) and your volume units consistent (mL, L, µL). The calculator returns C1 in the same concentration units as C2, plus the dilution factor.
The formula explained
Starting from \(C_1 \cdot V_1 = C_2 \cdot V_2\), divide both sides by V1 to isolate C1: $$C_1 = \frac{\text{Final Conc. (C2)} \times \text{Final Vol. (V2)}}{\text{Initial Vol. (V1)}}$$ Because concentration times volume equals total amount of solute, the equation simply states that the amount of solute is conserved during dilution — it is neither created nor destroyed, only spread into a larger volume.
Worked example
Suppose you diluted some stock to make 100 mL of a 0.5 M solution, and you used 10 mL of stock. Then $$C_1 = \frac{0.5 \times 100}{10} = \frac{50}{10} = 5\ \text{M}$$ The dilution factor is \(5 \div 0.5 = 10\times\), meaning the stock was diluted ten-fold.
FAQ
What units should I use? Any units, as long as both concentrations share one unit and both volumes share another. C1 comes out in the same units as C2.
What is the dilution factor? It is how many times more concentrated the stock was than the final solution, equal to \(C_1/C_2\) or equivalently \(V_2/V_1\).
Why does V1 have to be greater than zero? Dividing by zero volume is undefined — you must have used some measurable amount of stock.
