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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
Stock (initial) solution
M
mL
Final (desired) solution
M
mL
Volume of Stock (V₁)
–
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).
