Dilution Calculator
Stock and water volumes to make any weaker solution (C1V1 = C2V2).
What it does
Dilution keeps the solute while adding solvent: the moles pipetted from stock equal the moles in the finished flask. That conservation is the whole equation C1V1 = C2V2, with C for concentration and V for volume.
The tool above takes stock concentration, target concentration, and target milliliters. It returns the stock volume to pipette, the diluent to add, and the fold of the dilution.
The default turns 10 M stock into 1000 mL of 1 M: 100 mL of stock plus 900 mL of diluent, a 10x step. The same math chains into serial dilutions by feeding each tube as the next stock.
EPA lab methods and OpenStax Chemistry both run dilutions this way for standards and spikes. Both add the same bench rule: pipette stock into most of the diluent, mix, then top up to the calibration mark.
How to use
- Enter the stock bottle concentration.
- Enter the weaker concentration you need.
- Enter the final volume in milliliters.
- Read stock volume first for the pipette setting.
- Add it to most of the diluent, mix, then top up.
Formula
- C1
- Stock concentration on the bottle.
- C2, V2
- Wanted concentration and final volume.
- fold
- Stock over target: the x of the dilution.
Units must match between the two concentrations (both M, both %, both mg/L). Volumes then come out in whatever unit V2 used, milliliters here.
Worked example
Example: 10 M to 1 M, 1000 mL
Stock 10 M, target 1 M, final 1000 mL.
- Stock: 1 x 1000 / 10 = 100 mL.
- Diluent: 1000 - 100 = 900 mL.
- Fold: 10 / 1 = 10x.
- Bench: 100 mL stock into about 800 mL water, mix, top to 1000 mL.
- Tool shows 100 mL, 900 mL, 10x.
Reference table
| Target | Stock | Diluent |
|---|---|---|
| 0.1 M | 10 mL | 990 mL |
| 0.5 M | 50 mL | 950 mL |
| 1 M | 100 mL | 900 mL |
| 2 M | 200 mL | 800 mL |
Limits
- Target above stock is rejected; concentrate another way.
- Volumes add near ideally; dense mixes shift slightly.
- Pipette error dominates tiny stock volumes, so pre dilute first.
- Exotherms (acids) need slow addition with cooling.
Common mistakes
- Pouring water into concentrated acid instead of acid into water.
- Topping to solvent volume instead of final volume.
- Mixing units between percent and molarity.
- Pipetting 1 mL stock for a liter and trusting two digits.
- Skipping the mix before topping up.
Try it yourself
Quick checks. Answers sit tucked under each question.
5 M to 0.5 M, 500 mL?
Stock 50 mL, diluent 450 mL, 10x.
2 M to 0.5 M, 100 mL?
Stock 25 mL, diluent 75 mL, 4x.
Fold for 10 M to 0.1 M?
10 / 0.1 = 100x.
Questions
What is C1V1 = C2V2?
Moles conservation: stock conc times stock vol equals target conc times target vol.
How much stock for 1 M from 10 M?
One tenth of the final volume: 100 mL per liter.
What is a 10x dilution?
One part stock in ten total parts, a tenfold drop in concentration.
Can I dilute in steps?
Yes. Serial tens (1 mL to 9 mL, repeated) beat one giant jump for accuracy.
Why add acid to water?
Dilution heat dissipates safely in the larger water volume instead of erupting.
Do units need matching?
Concentrations must share units; the volume answer then follows V2 units.