Dilution Calculator
C1V1 = C2V2 with the honest door: dilution only thins. Take an aliquot of stock, make up to the mark, read the weaker truth.
Dilution Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Solute conserved — no reaction, volatilisation or buffering
- Volumes assumed additive to the mark
In short: 10 mL of 1 mol/L stock made up to 100 mL: C2 = 1 × 10 / 100 = 0.100000 mol/L. The dilution factor is 10×, and the water you actually added was 90 mL to reach the mark. Reverse the numbers — try to make 10 mL of something from 100 mL — and the page says what the flask would say: that is not dilution, that is wishing.
Formula
C1V1 = C2V2 · C2 = C1·V1/V2 · DF = V2/V1 · moles in the aliquot are conserved
Dilution moves moles, never creates them: the aliquot holds C1·V1 moles before and after, so the volume grows and the concentration pays the price. The dilution factor is how many times thinner the result is, and it is always V2/V1 — which is why a dilution pointing the other way is not a dilution at all.
Worked Example
- Enter the stock concentration.
- Enter the aliquot your pipette takes.
- Enter the final volume you make up to.
- Read the diluted concentration, the factor, and the water bill.
Defaults: 1 mol/L, 10 mL to 100 mL → 0.100000 mol/L, DF 10×, 90 mL of water. Reversed (100 mL stock into a 10 mL mark): refused — dilution only thins.
Strengths & Limits Of This Model
Where this engine is strong
- The concentrate door refused in words, not negative volumes
- Water bill printed against the mark
Where it stops
- Single-step only — chains live on the serial page
- No percent/molar translation built in
Practical Use Cases
Working standards
stock to bench strength
Assay prep
series points from one bottle
Teaching
conservation of moles, one flask wide
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Dilution Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why is C1V1 = C2V2 true?
Because the moles in the aliquot do not change when you add water: C1·V1 moles before, C2·V2 moles after, same moles. It is conservation, not a law of nature — a bookkeeping line for a move that loses nothing. Any three of the four quantities fix the fourth, which is why the equation survives every lab.
Can a dilution make a solution stronger?
No — and the page refuses to pretend otherwise. If the aliquot is bigger than the final volume, the arithmetic demands a HIGHER concentration than the stock, which is evaporation’s job, not dilution’s. The honest fix is upstream: a stronger stock, or more solute.
What is the dilution factor, exactly?
How many times thinner the new solution is: DF = V2/V1 = C1/C2. A DF of 10 means one part stock talks to nine parts water; a DF of 2 is a half-dilution. Factors multiply when you chain them, which is the serial-dilution page’s whole economy.
How much water do I add?
The mark decides: make up to V2, so the water is V2 − V1. Strictly, volumes are not perfectly additive — dissolving shifts things slightly — which is why the bench says ‘make up to the mark’ rather than ‘add exactly this much water’. The card prints the water bill; the mark has the final word.
Do the units have to match on both sides?
Within each pair, yes: V1 and V2 in the same unit, C1 and C2 in the same unit. The equation cancels them, so mL in, mL out — but mixing mL with L on one side of the same pair is the classic thousand-fold error. This page keeps mL everywhere and shows the division in the open.
Why is my diluted pH not what I calculated?
Because pH is not a conserved quantity — it rides the hydrogen ion, which buffers, hydrolyses and generally misbehaves when diluted. C1V1 = C2V2 prices CONCENTRATION, and only for solutes that stay themselves in water. The pH page takes that question on with its own honesty cards.
What if my stock is a percent, not a molar?
Convert first or keep everything in percent — the equation only asks that C1 and C2 speak the same language. The percent-solution and solution-concentration pages run the conversions; enter the translated stock here and the dilution arithmetic is identical.
How does this chain into serial dilutions?
A serial dilution is this page, repeated: each tube’s output is the next tube’s stock, and the factors multiply into the total. Ten-fold steps chained seven deep thin the original a 10,000,000-fold. The serial-dilution page runs the whole rack at once and prices the ladder.