N₁V₁ = N₂V₂ Dilution Calculator

Solve for any missing value — stock concentration, stock volume, final concentration, or final volume — using the N₁V₁ = N₂V₂ (C₁V₁ = C₂V₂) dilution relationship, for preparing reagents, buffers, and standards from a stock.

Dilution details

Solve for

Pick the value you don't know — enter the other three below.

Units

Stock (initial) solution

Concentration of stock (N₁)

Volume of stock (V₁)

Final (desired) solution

Desired final concentration (N₂)

Final total volume (V₂)

Volume of Stock (V₁)

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Any consistent concentration unit works (molarity, normality, %, mg/mL, fold) as long as N₁ and N₂ use the same unit. Always confirm with your lab's validated SOP before preparing reagents.

Common Dilution Ratios (tap to load, per 100 units)

Half Dilution

1:2

50% of original strength

Fifth Dilution

1:5

20% of original strength

Tenfold Dilution

1:10

Common stock working dilution

50× Dilution

1:50

Dilute concentrated stocks

Hundredfold Dilution

1:100

Standard curve, ELISA

Thousandfold Dilution

1:1000

High-titer stocks, antibodies

Formulas

N₁ × V₁ = N₂ × V₂ V₁ = (N₂ × V₂) ÷ N₁ N₂ = (N₁ × V₁) ÷ V₂ V₂ = (N₁ × V₁) ÷ N₂

About N₁V₁ = N₂V₂

This relationship describes how a solution's concentration and volume trade off when it is diluted: N₁ and V₁ are the concentration and volume of the starting (stock) solution, and N₂ and V₂ are the concentration and volume of the final (diluted) solution. Because the total amount of solute doesn't change on dilution — only its volume does — the product of concentration × volume stays constant on both sides. The equation works with any concentration unit (molarity, normality, %, mg/mL, or fold) as long as N₁ and N₂ are expressed in the same unit.

How to prepare a dilution

Solve for V₁ to find how much stock solution to measure out.
Measure that volume of stock into your final container.
Add diluent (e.g. water or buffer) until the total volume reaches V₂ — don't just add V₂ of diluent on top of the stock.
Mix thoroughly before use, and label with the final concentration, date, and preparer.

Notes and limitations

This calculator assumes ideal mixing with no significant volume contraction or expansion; for precise reagent work, always follow your lab's validated SOP.
For a multi-step serial dilution, apply this calculator once per step, using the previous step's N₂ as the next step's N₁.
For preparing a % w/v, % w/w, or % v/v solution from pure solute rather than diluting a stock, use a percentage solution calculator instead.
Always label prepared reagents with concentration, preparation date, and expiry per your quality management system (e.g. ISO 15189).