Dilution Calculator
Calculate any dilution using C₁V₁ = C₂V₂. Enter three values and solve for the fourth — find stock volume needed, final concentration, or dilution factor instantly.
mL
Enter your values above to see the results.
Tips & Notes
- ✓Always add concentrated solution to diluent (not diluent to concentrate) when mixing — for acids especially, the exothermic heat is absorbed by the larger volume of diluent, preventing dangerous splattering.
- ✓For serial dilutions, each step multiplies the dilution factor. Three consecutive 1:10 dilutions give a final factor of 1:1000 (10⁻³). Serial dilution is more accurate than a single large dilution for factors above 100×.
- ✓Verify your dilution by checking: C₂ must be less than C₁; V₂ must be greater than V₁; V₁ (stock added) = V₂ − volume of diluent added. If any of these fail, check your inputs.
- ✓For cell culture media, prepare 10× concentrated stock solutions of buffers and supplements, then dilute 1:10 with water for each use — reduces preparation time and storage volume by 90%.
- ✓When diluting with concentrated units (mM to µM, M to mM), convert both concentrations to the same unit first. 1 mM stock diluted to 10 µM: convert — 1,000 µM to 10 µM needs a 100× dilution.
Common Mistakes
- ✗Confusing V₁ (volume of stock to add) with V₂ (total final volume) — V₁ is what you pipette from stock; V₂ is the total solution you end up with. If V₂ = 100 mL and V₁ = 10 mL, you add 90 mL of diluent, not 100 mL.
- ✗Using different units for C₁ and C₂ — both concentrations must be in the same unit (both M, both mg/mL, or both %) before applying C₁V₁ = C₂V₂. Mixing mM and M without converting gives 1,000× errors.
- ✗Applying C₁V₁ = C₂V₂ to solutions that react with water — this equation only applies to non-reactive dilutions. Diluting concentrated H₂SO₄ in water is exothermic and requires special safety precautions beyond just calculating volumes.
- ✗Forgetting that the equation assumes ideal mixing — for very viscous solutions or solutions with significant density differences, the actual volume after mixing may differ from V₁ + V diluent. Make up to volume in a volumetric flask.
- ✗Rounding V₁ too aggressively — if the calculation gives 41.7 mL of stock, rounding to 40 mL introduces a 4.1% error in final concentration. Use calibrated pipettes or burettes to achieve the precision the calculation implies.
Dilution Calculator Overview
Dilution is one of the most frequently performed operations in any analytical, clinical, or research laboratory. The C₁V₁ = C₂V₂ equation is the algebraic expression of a simple principle: the number of moles of solute is conserved when you add more solvent. Mastering this equation — and knowing when it does and does not apply — is essential for accurate solution preparation.
Core dilution equation:
C₁V₁ = C₂V₂ | Dilution Factor = C₁/C₂ = V₂/V₁
EX: Need 500 mL of 0.1 M HCl from a 12 M concentrate. V₁ = (0.1 × 500) / 12 = 4.17 mL. Transfer 4.17 mL of 12 M HCl to a 500 mL volumetric flask containing ~400 mL water, then fill to mark. Add acid to water — never reverse.Serial dilution — cumulative factors:
Final Concentration = C₀ × (1/DF)^n | where DF = dilution factor per step, n = number of steps
EX: 3 serial 1:5 dilutions from 1 M stock → Final = 1 M × (1/5)³ = 1 M × 0.008 = 0.008 M = 8 mM. V₁ each step = 1 mL into 4 mL diluent (1 part stock + 4 parts water = 1:5 total dilution).Common dilution series — stock to working concentration:
| Stock (C₁) | Target (C₂) | Dilution Factor | V₁ for 1 mL final | Diluent to add |
|---|---|---|---|---|
| 1 M | 100 mM | 10× | 100 µL | 900 µL |
| 1 M | 10 mM | 100× | 10 µL | 990 µL |
| 1 M | 1 mM | 1,000× | 1 µL | 999 µL |
| 10 mM | 100 µM | 100× | 10 µL | 990 µL |
| 10 mM | 10 µM | 1,000× | 1 µL | 999 µL |
| 10 mg/mL | 1 µg/mL | 10,000× | 0.1 µL (serial preferred) | — |
| Situation | Equation Valid? | Notes |
|---|---|---|
| Aqueous buffer dilution | ✅ Yes | Standard application |
| Drug stock dilution in media | ✅ Yes | Watch DMSO % final |
| Concentrated acid in water | ✅ Yes (calculation) | ⚠ Add acid to water — safety |
| Solutions that react with water | ❌ No | Hydrolysis changes solute |
| Mixing two different solvents | ❌ Approximate | Volume is not additive |
| Very dense solutions (>30% w/v) | ❌ Approximate | Volume changes on mixing |
Frequently Asked Questions
C₁V₁ = C₂V₂ expresses conservation of moles of solute during dilution. The number of moles in the stock (C₁ × V₁) equals the moles in the diluted solution (C₂ × V₂) because dilution adds solvent but not solute. To find any unknown: rearrange algebraically. V₁ = C₂V₂/C₁ (stock volume needed); C₂ = C₁V₁/V₂ (final concentration); V₂ = C₁V₁/C₂ (total volume needed). The equation works with any consistent concentration units — M, mM, µM, mg/mL, % — as long as both concentrations use the same unit.
Dilution factor = C₁/C₂ = V₂/V₁ — the ratio by which the concentration decreases. A 1:10 dilution has a dilution factor of 10 (concentration decreases 10-fold). Example: 1 mL of 10 mM stock added to 9 mL of water gives 10 mL total of 1 mM — dilution factor = 10. In serial dilutions, dilution factors multiply: 1:10 followed by 1:10 gives 1:100 total dilution. In microbiology, dilution factors are used to calculate original sample concentration from colony counts: concentration = colonies / (volume plated × dilution factor).
A 1:10 dilution means 1 part stock in 10 parts total (not 1 part stock plus 10 parts water). To make 10 mL of 1:10 dilution: take 1 mL of stock and add 9 mL of diluent. Final volume = 10 mL, concentration = 1/10 of original. Common mistake: adding 10 mL of diluent to 1 mL of stock gives 11 mL total — a 1:11 dilution, not 1:10. The distinction matters in microbiology plate counts where dilution factors directly affect the calculated cell concentration. Always specify total volume (V₂), not the diluent volume added.
Serial dilution: perform repeated dilutions, each using the previous diluted solution as the new "stock." Example: 10-fold serial dilution starting at 1 M. Step 1: 1 mL of 1 M + 9 mL water = 10 mL of 0.1 M (10⁻¹ dilution). Step 2: 1 mL of 0.1 M + 9 mL water = 10 mL of 0.01 M (10⁻² dilution). Step 3: → 0.001 M (10⁻³). Final concentration = initial concentration × (dilution factor)^number of steps. For accurate serial dilutions: change pipette tips between steps, vortex or mix each tube thoroughly before transferring, and use fresh tubes at each step.
C₁V₁ = C₂V₂ works with any concentration unit as long as both sides use the same unit. Compatible units: molar (M, mM, µM, nM); mass concentration (mg/mL, µg/mL, ng/mL); percent (% w/v, % v/v); parts per million (ppm) or per billion (ppb). The volume units (V₁ and V₂) must also be consistent — both in mL, both in L, or both in µL. If you have C₁ in M and C₂ in mM, convert to the same unit first: 1 M = 1,000 mM. The equation fails for reactive dilutions and does not account for volume of mixing for dense solutions.
Example: you have a 10 mM drug stock in DMSO and need 10 µM final concentration in 2 mL cell culture media. First convert: 10 mM = 10,000 µM. Apply C₁V₁ = C₂V₂: V₁ = (10 µM × 2 mL) / 10,000 µM = 0.002 mL = 2 µL. Add 2 µL of stock to 1.998 mL of media for 2.000 mL total. Note: 2 µL DMSO in 2 mL = 0.1% DMSO — verify this is below the DMSO tolerance of your cell line (typically ≤0.1% for most mammalian cells). If DMSO percentage is too high, prepare an intermediate aqueous dilution first.