Dilution Factor Calculator
Solve C₁V₁ = C₂V₂ equations, calculate dilution ratios (1:10, 1:50), serial and double dilutions, and find any dilution factor instantly — with a complete recipe box showing exactly how to prepare your solution.
Enter any 3 values and select which variable to solve for. The calculator rearranges C₁V₁ = C₂V₂ and solves instantly.
V₁ =
—Enter solute and solvent volumes to calculate the dilution ratio, dilution factor, and percentage concentration — for any mixing ratio including 1:10 and 1:50 dilutions.
Calculate the final concentration after multiple sequential dilution steps. Used for cell dilutions, bacterial plating, antibody titrations, and double dilution protocols.
| Step | DF This Step | Cumulative DF | Concentration After Step |
|---|
Enter initial and final concentrations to instantly find the dilution factor (DF). Works for any unit — M, mM, mg/mL, µg/mL, % — as long as both are compatible.
Dilution Factor (DF)
—How to Calculate Dilution Factor — Formula and Method
The dilution factor (DF) is a fundamental quantity in chemistry, biology, and laboratory science. It tells you how many times more dilute the final solution is compared to the original stock. The dilution factor formula has two equivalent forms:
Worked Example — 1:50 Dilution (how to find dilution factor)
Step-by-step: 1:50 dilution factor calculation
- V_initial (solute) = 1 mL
- Solvent added = 49 mL
- V_final = 1 + 49 = 50 mL total
- DF = V_final / V_initial = 50 / 1 = 50
- Final concentration = Starting concentration ÷ 50 = 2% of original
⚠️ Key distinction: "1:50" = 1 part solute in 50 parts TOTAL (1 part + 49 parts solvent). DF = 50. Do not confuse with "1 to 50 parts solvent" which gives 51 parts total and DF = 51.
| Notation | Solute | Solvent Added | Total Volume | DF | % Conc. |
|---|---|---|---|---|---|
| 1:2 | 1 | 1 | 2 | 2 | 50% |
| 1:5 | 1 | 4 | 5 | 5 | 20% |
| 1:10 | 1 | 9 | 10 | 10 | 10% |
| 1:50 | 1 | 49 | 50 | 50 | 2% |
| 1:100 | 1 | 99 | 100 | 100 | 1% |
| 1:1000 | 1 | 999 | 1000 | 1000 | 0.1% |
Using the C1V1 = C2V2 Formula (c1v1 c2v2)
The C1V1 = C2V2 equation is the standard formula for preparing a diluted solution from a concentrated stock. It is derived from conservation of moles — the amount of solute before dilution equals the amount after.
✅ Validation rule: V₂ must always be ≥ V₁. You cannot have a final volume smaller than the stock you started with. Diluent volume = V₂ − V₁ must be ≥ 0. If V₁ > V₂, the target concentration is impossible by dilution — it would require concentrating, not diluting.
Example — Prepare 100 mL of 0.1 M NaCl from 1 M stock
- C₁ = 1 M, C₂ = 0.1 M, V₂ = 100 mL, V₁ = ?
- V₁ = (C₂ × V₂) / C₁ = (0.1 × 100) / 1 = 10 mL of stock
- Diluent = V₂ − V₁ = 100 − 10 = 90 mL water
- DF = C₁ / C₂ = 1 / 0.1 = 10 (1:10 dilution)
Dilution Ratio vs. Dilution Factor — The Key Difference
The dilution ratio and dilution factor are closely related but describe different things. Understanding the difference is essential when using a dilution ratio calculator or reading a protocol.
💡 Modern convention (this calculator): 1:10 = 1 part solute in 10 parts TOTAL. Solvent = 9 parts. DF = 10. Concentration = 10% of original.
⚠️ Older convention: 1:10 sometimes means 1 part solute PLUS 10 parts solvent = 11 total. DF = 11. Always check your protocol's convention!
The percentage concentration = (1 / DF) × 100. For a 1:50 dilution (DF = 50): concentration = 2%. For a dilution 10:1 (concentrate, not dilution): the solution is 10× more concentrated than the diluent.
Serial Dilution and Double Dilution Calculations
A serial dilution (dilution series) is a stepwise sequence where each step dilutes the previous result. The double dilution calculation is two sequential steps. Used in cell dilution for bacterial counts, antibody titrations, and drug concentration curves.
Double dilution — achieving 1:1000 in two steps
- Step 1: Take 1 mL stock + add 99 mL water → 1:100 dilution (DF₁ = 100)
- Step 2: Take 1 mL from Step 1 + add 9 mL water → 1:10 dilution (DF₂ = 10)
- Total DF = 100 × 10 = 1,000
- If C₀ = 1 M → Final = 1 M / 1000 = 1 mM
Worked Examples — 8 Step-by-Step Problems
1. Finding V₁ for a molar solution
- Problem: Prepare 250 mL of 150 mM NaCl from a 5 M stock.
- Convert: C₁ = 5 M = 5000 mM, C₂ = 150 mM, V₂ = 250 mL
- V₁ = (150 × 250) / 5000 = 7.5 mL stock
- Diluent = 250 − 7.5 = 242.5 mL water
2. Converting mg/mL concentrations
- Problem: Make 5 mL of 0.5 mg/mL BSA from a 10 mg/mL stock.
- V₁ = (0.5 × 5) / 10 = 0.25 mL = 250 µL stock
- Diluent = 5 − 0.25 = 4.75 mL buffer
- DF = 10 / 0.5 = 20 (1:20 dilution)
3. Calculating 1:1000 ratio in two steps (double dilution)
- Step 1: 1:100 → 10 µL antibody + 990 µL buffer (DF = 100)
- Step 2: 1:10 → 100 µL from Step 1 + 900 µL buffer (DF = 10)
- Total DF = 100 × 10 = 1,000
- Stock at 1 mg/mL → final = 1 µg/mL
4. Finding the final concentration of a 1:50 dilution
- Problem: 200 µM drug solution after 1:50 dilution.
- DF = 50
- Final = 200 µM / 50 = 4 µM
- Recipe: 1 mL drug + 49 mL solvent = 50 mL total at 4 µM
5. Solving for C₂ (what concentration results?)
- Add 5 mL of 100 mM solution to 50 mL total. C₂ = ?
- C₂ = (C₁ × V₁) / V₂ = (100 × 5) / 50 = 10 mM
- DF = 50 / 5 = 10
6. Finding DF from two mg/mL values
- Stock = 8 mg/mL, measured result = 0.4 mg/mL
- DF = 8 / 0.4 = 20 (1:20 dilution)
- % Concentration = 100/20 = 5%
7. Three-step serial dilution with varying DFs
- Start: 1 M glucose. Steps: 1:10, 1:5, 1:2
- After Step 1: 1 M / 10 = 100 mM (DF = 10)
- After Step 2: 100 mM / 5 = 20 mM (DF = 50)
- After Step 3: 20 mM / 2 = 10 mM (Total DF = 100)
8. Preparing a working solution from % concentration
- Problem: Make 200 mL of 30% ethanol from 70% stock.
- V₁ = (30 × 200) / 70 = 85.71 mL of 70% ethanol
- Water = 200 − 85.71 = 114.29 mL water
- DF = 70 / 30 ≈ 2.33