Answer first
What this calculator tells you
Calculate the stock volume and diluent needed to reach a target concentration. Prepare a solution to a target strength from a stock you already have. Formula: C₁ × V₁ = C₂ × V₂, so V₁ = C₂ × V₂ ÷ C₁; diluent = V₂ − V₁. At the worked-example inputs, the stock volume to use (v₁) is 62.5. Holding every other input steady, moving stock concentration (c₁) from 10 to 14 moves the result from 53.6 to 75.
Transparent method
The formula
Prepare a solution to a target strength from a stock you already have.
Worked example
Example inputs
How to interpret the result
Diluting a solution keeps the amount of the dissolved substance fixed while the volume grows, so concentration times volume stays equal before and after. To make 500 milliliters at 1.5 from a stock at 12, you need 62.5 milliliters of stock and 437.5 of diluent. The same relation covers cleaning concentrates, lab reagents and garden sprays.
At the worked-example inputs the stock volume to use (v₁) is 62.5. It rises with final volume (v₂) and target concentration (c₂) and falls as stock concentration (c₁) increases.
These are exact physics and chemistry formulas. Real-world results add tolerances from component quality, temperature and measurement error that this calculator does not model.
Before you rely on it
What to check
Add the stock to the diluent up to the final volume, not the other way around by volume. The final volume is what counts, not the volume of water added.
The common error
Where people go wrong with dilution calculator
Adding the full final volume of water to the stock. That overshoots the volume and leaves the solution weaker than the target.
Sensitivity evidence
How stock concentration (c₁) changes the stock volume to use (v₁)
Holding every other input at the worked-example value, moving stock concentration (c₁) from 10 to 14 moves the stock volume to use (v₁) from 53.6 to 75: a spread of 21.4, or 34% of the worked-example result.
| Stock concentration (C₁) | Stock volume to use (V₁) | Diluent to add |
|---|---|---|
| 10 | 75 | 425 |
| 11 | 68.2 | 431.8 |
| 12worked example | 62.5 | 437.5 |
| 13 | 57.7 | 442.3 |
| 14 | 53.6 | 446.4 |
Every input, tested
Which input moves the stock volume to use (v₁) most
Of the 3 inputs, final volume (v₂) moves the stock volume to use (v₁) most (12.5 across the range tested) and stock concentration (c₁) moves it least (10.5).
| Input | Tested from | To | Stock volume to use (V₁) at each end | Swing |
|---|---|---|---|---|
| Final volume (V₂) | 450 | 550 | 56.3 to 68.8 | 12.5 (20%) |
| Target concentration (C₂) | 1.4 | 1.7 | 58.3 to 70.8 | 12.5 (20%) |
| Stock concentration (C₁) | 11 | 13 | 68.2 to 57.7 | 10.5 (17%) |
Two variables at once
Stock volume to use (V₁) by stock concentration (c₁) and target concentration (c₂)
Across the grid the stock volume to use (v₁) runs from 42.9 to 90. Moving stock concentration (c₁) from 10 to 14 shifts it by 21.4 at the middle column, and moving target concentration (c₂) from 1.2 to 1.8 shifts it by 25 at the middle row, so target concentration (c₂) is the bigger lever here.
| Stock concentration (C₁) \ Target concentration (C₂) | 1.2 | 1.5 | 1.8 |
|---|---|---|---|
| 10 | 60 | 75 | 90 |
| 11 | 54.5 | 68.2 | 81.8 |
| 12 | 50 | 62.5 | 75 |
| 13 | 46.2 | 57.7 | 69.2 |
| 14 | 42.9 | 53.6 | 64.3 |
The highlighted cell is the worked example: 62.5.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Stock concentration (C₁) | 12 | Enter the stock concentration (c₁) used in this calculation. |
| Target concentration (C₂) | 1.5 | In the same unit as the stock concentration. |
| Final volume (V₂) | 500 | The total volume you want to end up with, in any unit. |
| Stock volume to use (V₁) | 62.5 | |
| Diluent to add | 437.5 | |
Inputs, definitions and assumptions
Stock concentration (C₁)
Enter the stock concentration (c₁) used in this calculation. The prefilled worked-example value is 12.
Target concentration (C₂)
In the same unit as the stock concentration. The prefilled worked-example value is 1.5.
Final volume (V₂)
The total volume you want to end up with, in any unit. The prefilled worked-example value is 500.
How to use this calculator
- 1Verify the inputs. Gather stock concentration (c₁), target concentration (c₂) and final volume (v₂) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the stock volume to use (v₁) at 62.5. Store your own version of it as Scenario A.
- 3Test one change. Start with final volume (v₂), the input with the biggest effect here: moving final volume (v₂) from 450 to 550 takes the stock volume to use (v₁) from 56.3 to 68.8, a swing of 20% of the worked-example figure.
- 4Check the extremes. At half the example final volume (v₂) (250) the stock volume to use (v₁) is 31.3; at double (1,000) it is 125.
People also ask
Frequently asked questions
How do you calculate dilution?
C₁ × V₁ = C₂ × V₂, so V₁ = C₂ × V₂ ÷ C₁; diluent = V₂ − V₁. At the worked-example inputs the stock volume to use (v₁) is 62.5.
What does the dilution result mean?
Prepare a solution to a target strength from a stock you already have. At the worked-example inputs the stock volume to use (v₁) is 62.5. It rises with final volume (v₂) and target concentration (c₂) and falls as stock concentration (c₁) increases.
How much does stock concentration (c₁) change the stock volume to use (v₁)?
Holding every other input at the worked-example value, moving stock concentration (c₁) from 10 to 14 moves the stock volume to use (v₁) from 53.6 to 75, a spread of 21.4.
What are the limits of this dilution calculator?
These are exact physics and chemistry formulas. Real-world results add tolerances from component quality, temperature and measurement error that this calculator does not model. The tables on this page test stock concentration (c₁) only from 10 to 14; a value outside that range is not tabulated here.
Which input moves the stock volume to use (v₁) most in the dilution calculator?
Ranked by how far each moves the stock volume to use (v₁) across the range tested: final volume (v₂) (12.5, 20%), target concentration (c₂) (12.5, 20%) and stock concentration (c₁) (10.5, 17%).
If I double final volume (v₂) in the dilution calculator, does the stock volume to use (v₁) double?
Doubling it from 500 to 1,000 takes the stock volume to use (v₁) from 62.5 to 125, which is 2.00 times the worked-example figure. So the result scales almost exactly in proportion. Halving it to 250 gives 31.3.
How much does target concentration (c₂) matter in the dilution calculator?
The worked example uses 1.5. Holding every other input at its worked-example value, moving target concentration (c₂) from 1.4 to 1.7 takes the stock volume to use (v₁) from 58.3 to 70.8, a swing of 20% of the worked-example figure.
How much does final volume (v₂) matter in the dilution calculator?
The worked example uses 500. With the other inputs left at the worked example, moving final volume (v₂) from 450 to 550 takes the stock volume to use (v₁) from 56.3 to 68.8, a swing of 20% of the worked-example figure.
Which inputs change the diluent to add in the dilution calculator?
At the worked-example inputs it is 437.5. Stock concentration (c₁) takes it from 431.8 to 442.3, target concentration (c₂) takes it from 441.7 to 429.2 and final volume (v₂) takes it from 393.8 to 481.3.
How do I dilute a solution accurately?
Put the measured stock volume in a container, then add diluent up to the final volume mark, instead of adding a fixed volume of water. Filling to the mark keeps the final volume, and so the concentration, correct.
Why is the resistor tolerance band on the right?
By convention the tolerance band is set apart from the other bands, so you read from the other end. Gold and silver, the usual tolerance colors, are never used as the first digit.
Sources and evidence
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