Dilution Calculator
Enter any three of stock concentration, stock volume, target concentration and target volume to solve for the fourth using M1V1 = M2V2.
M1V1 = M2V2, so Stock volume = 50.0000.
What Is Dilution?
Diluting a solution means adding more solvent without adding more solute -- the total moles of dissolved substance stay exactly the same, just spread through more liquid, which lowers the concentration. That's why M1V1 (moles before) equals M2V2 (moles after): nothing was added or removed except solvent.
This equation solves for any one of the four values given the other three -- most often V1, the amount of concentrated stock solution you need to measure out to make a target volume at a target concentration.
Worked example
How much 6 M stock solution is needed to make 250 mL of a 0.5 M solution?
M1V1 = M2V2, so V1 = M2V2 / M1 = (0.5 x 250) / 6 = 20.83 mL of stock.
Add water until the total volume reaches 250 mL (about 229.17 mL of water), not 250 mL of water on top of the stock.
Common mistake
Adding V2 worth of water instead of V2 minus V1. The final volume V2 already includes the stock solution's own volume -- so the water added is always V2 − V1, not V2.
Keep going
- Dilution starts from a known stock molarity; the molarity calculator is where you'd work that starting concentration out from moles and volume. Molarity Calculator
- Molarity and molality both measure concentration but by different denominators (solution volume vs. solvent mass); the molality calculator uses the mass-based definition. Molality Calculator
Frequently Asked Questions
What does M1V1 = M2V2 mean?
It's the dilution equation: the moles of solute before dilution (M1 x V1) equal the moles of solute after (M2 x V2), because diluting a solution adds solvent, not more solute. M1/V1 are the stock (starting) concentration and volume; M2/V2 are the target (final) concentration and volume.
Do V1 and V2 need to be in liters?
No -- any volume unit works as long as V1 and V2 use the SAME unit (both mL, or both L). The equation is a ratio, so the units cancel out. Molarity (M1, M2) does need to stay in mol/L for the result to be a real molarity.
How much water do I add?
The volume of solvent (usually water) to add is V2 minus V1 -- the final volume minus the stock volume you started with, not V2 by itself. For example, diluting 50 mL of stock to a final 500 mL means adding 450 mL of water, not 500 mL.
What if I want to dilute to a specific ratio, like 1:10?
A 1:10 dilution means the final concentration is 1/10th the stock concentration, so M2 = M1/10. Set M2 to that value (or just enter V2 = 10 x V1 for the same result) and solve for whichever volume you need.
Can this calculator handle serial dilutions?
Not directly in one step, but each step of a serial dilution is just this same M1V1 = M2V2 equation applied again, using the previous step's M2 as the next step's M1.
Related Calculators
- Molarity Calculator — Solutions & Concentration
- Molality Calculator — Solutions & Concentration
- Molar Mass Calculator — Atomic & Molecular
- Moles Calculator — Atomic & Molecular