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Dilution Calculator: C1V1 = C2V2, Dilution Ratios and Mixing

How the dilution calculator works: C₁ · V₁ = C₂ · V₂. To make 500 mL of 70 % alcohol from 96 %, take 70 · 500 / 96 = 365 mL and top up with water to 500 mL. It also handles ratios such as 1:50 and mixing two concentrations.

Example: What do you want to calculate: How much stock for a target concentration? · Concentration unit: % · Volume unit: millilitres (mL) · Stock concentration C₁ 96 · Target concentration C₂ 70 · Final volume V₂ 500 → Result: 364.6 mL stock + 135.4 mL water. Source: OpenStax, OpenStax Chemistry 2e, 3.3 Molarity – Dilution of Solutions (C₁V₁ = C₂V₂). Updated: .

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Result

Result
364.6 mL stock + 135.4 mL water
Values
QuantityValue
Stock solution V₁364.6 mL
Water / diluent135.4 mL
Dilution ratio1 : 1.371
Step by step
  • V₁ = C₂ · V₂ / C₁ = 70 % · 500 mL / 96 % = 364.6 mL
  • Water = V₂ − V₁ = 500 mL − 364.6 mL = 135.4 mL
Ethanol and water shrink slightly when mixed (volume contraction), so the final volume is a little less than the sum – measure with an alcoholmeter if precision matters.

How it is calculated

The dilution formula C₁V₁ = C₂V₂

When you dilute, the amount of dissolved substance stays the same while the volume grows, so:

C₁ · V₁ = C₂ · V₂  ·  rearranged: V₁ = C₂ · V₂ / C₁  and  C₂ = C₁ · V₁ / V₂

Any concentration unit works (%, mg/mL, mol/L) as long as both concentrations use the same one – the same goes for volumes.

Example: 70 % alcohol from 96 %

  1. V₁ = 70 · 500 mL / 96 = 364.6 mL of 96 % alcohol
  2. Top up with water to 500 mL (about 135 mL of water).

Dilution ratio 1:50 – two readings

“1:50” usually means 1 part concentrate + 50 parts water (51 parts in total). Some manufacturers mean 1 part in 50 parts total. For 5 L of cleaning solution that is 98 mL or 100 mL of concentrate – with small ratios like 1:3 the difference is bigger (1.25 L vs 1.67 L). The calculator shows both.

RatioConcentrate for 1 L (1 + x parts)for 5 L
1:1090.9 mL454.5 mL
1:2047.6 mL238.1 mL
1:4024.4 mL122 mL
1:5019.6 mL98 mL
1:1009.9 mL49.5 mL

Mixing two solutions (Pearson square)

To mix solutions with concentrations A and B to a target Z, the Pearson square (alligation) gives the ratio: parts of A = Z − B, parts of B = A − Z. Example: 40 % and 10 % to 20 % → 10 : 20 = 1 : 2. For water use B = 0.

Limitations

The calculation assumes volumes are additive, which is not exactly true for ethanol and water or for very concentrated acids. Medication and infusion dosing follows medical and pharmaceutical rules – this calculator is not meant for that.

Frequently asked questions

How do you calculate a dilution?

With C₁V₁ = C₂V₂. To make 1 L of 0.1 M solution from 1 M stock: V₁ = 0.1 · 1000 / 1 = 100 mL, then add water to 1000 mL.

How do you calculate a percent dilution?

Concentrate = target % · final volume / stock %. 1 L of 3 % from 30 %: 3 · 1000 / 30 = 100 mL concentrate + 900 mL water.

What does a 1:50 dilution mean?

Usually 1 part concentrate to 50 parts water – 20 mL per litre of water, or 98 mL for 5 L of finished solution. Some labels mean 1 part in 50 parts total (100 mL for 5 L).

How do you dilute mg/mL?

Use the same formula in mg/mL: from 50 mg/mL to 2 mg/mL, 100 mL needs 2 · 100 / 50 = 4 mL of stock plus 96 mL of diluent.

What is the dilution factor?

Final volume divided by stock volume, or stock concentration divided by final concentration. 100 mL made up to 1 L is a dilution factor of 10 – in the lab often written 1:10, meaning 1 part in 10 parts total.

Sources and legal basis

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