Dilution Calculator — C1V1 = C2V2 Formula
The C1V1 = C2V2 dilution equation is the cornerstone formula used in chemistry, biology, and pharmacology to calculate how to dilute a concentrated stock solution to a desired working concentration. Here, C1 is the initial concentration, V1 is the volume of stock solution needed, C2 is the target concentration, and V2 is the final total volume after dilution. The formula works for any concentration unit (molarity M, percent %, mg/mL, ppm) as long as both sides use the same units. Use it whenever you need to prepare buffer solutions, reagent dilutions, IV drug infusions, or serial dilutions in the lab.
The dilution formula C1V1 = C2V2 states that moles of solute are conserved: initial concentration × initial volume = final concentration × final volume. To find the final volume needed: **V2 = (C1 × V1) / C2**. For example, diluting 10 mL of a 1 M solution to 0.1 M requires V2 = (1 × 10) / 0.1 = **100 mL total** — add 90 mL of solvent to the original 10 mL. Works with any consistent concentration unit (M, %, mg/mL, ppm).
When to use this calculator
- Preparing a 0.1 M NaCl working solution from a 5 M stock for cell culture experiments.
- Calculating the correct volume of bleach (sodium hypochlorite 8.25%) to add to water to achieve a 0.5% disinfectant solution per CDC guidelines.
- Determining how many mL of a 50 mg/mL drug stock vial to draw and dilute for an IV infusion at 2 mg/mL in 250 mL saline.
- Making a 1:10 serial dilution series for a bacterial plate count assay (e.g., 1 mL sample into 9 mL diluent, repeated 5×).
- Mixing a 70% ethanol stock with distilled water to produce 500 mL of 30% ethanol for tissue fixation.
- Diluting a 1000 ppm nitrate standard to prepare 100 ppm, 50 ppm, and 10 ppm calibration standards for a colorimetric assay.
Worked Example: 1 M NaCl → 0.1 M
- Given: C1 = 1 M (stock), V1 = 10 mL (volume to take), C2 = 0.1 M (target)
- Solve for V2: V2 = (C1 × V1) / C2 = (1 × 10) / 0.1 = 100 mL
- Volume of solvent to add: V2 − V1 = 100 − 10 = 90 mL of distilled water
How it works
3 min readHow the C1V1 = C2V2 Dilution Formula Works
The dilution equation is derived from the conservation of moles of solute: the amount of solute present before and after dilution is the same — you are only adding more solvent.
C1 × V1 = C2 × V2
Rearrangements:
V2 = (C1 × V1) / C2 ← final volume needed
V1 = (C2 × V2) / C1 ← stock volume to take
C2 = (C1 × V1) / V2 ← resulting concentration
Volume of solvent to ADD = V2 − V1> Units rule: C1 and C2 must share the same unit (both M, both %, both mg/mL, etc.). V1 and V2 must share the same unit (both mL or both L). Do NOT mix mL with L in the same calculation.
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Quick Reference Table — Common Dilutions
Pre-calculated values for the most frequent lab and household scenarios:
| Stock C1 | Target C2 | Stock Vol V1 | Final Vol V2 | Solvent to Add |
|---|---|---|---|---|
| 1 M | 0.1 M | 10 mL | 100 mL | 90 mL |
| 5 M NaCl | 0.15 M | 3 mL | 100 mL | 97 mL |
| 70% EtOH | 30% | 214 mL | 500 mL | 286 mL |
| 8.25% NaOCl (bleach) | 0.5% | 60.6 mL | 1000 mL | 939.4 mL |
| 1000 ppm NO₃⁻ | 100 ppm | 10 mL | 100 mL | 90 mL |
| 50 mg/mL drug | 2 mg/mL | 10 mL | 250 mL | 240 mL |
| 100× PBS buffer | 1× | 10 mL | 1000 mL | 990 mL |
| 37% HCl (w/w) | ~1 M | 8.3 mL | 100 mL | 91.7 mL |
| 12 M HCl | 0.1 M | 0.83 mL | 100 mL | 99.17 mL |
| 10% stock | 1% | 10 mL | 100 mL | 90 mL |
All volumes are approximate; always verify with a calibrated volumetric flask.
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Typical Cases
Case 1 — Cell Culture Buffer (Molarity)
You have a 5 M NaCl stock and need 100 mL of 0.15 M NaCl (isotonic saline).
V1 = (C2 × V2) / C1
V1 = (0.15 M × 100 mL) / 5 M
V1 = 3 mLPipette 3 mL of 5 M NaCl into a 100 mL volumetric flask and fill to the mark with distilled water.
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Case 2 — Disinfectant Preparation (Percent)
CDC recommends a 0.5% sodium hypochlorite solution for surface disinfection. Your household bleach is 8.25% NaOCl. You want 1 liter.
V1 = (0.5% × 1000 mL) / 8.25%
V1 = 60.6 mL bleach → add to 939.4 mL water---
Case 3 — Serial Dilution (Microbiology)
A 1:10 serial dilution transfers 1 mL of sample into 9 mL of diluent. Each step:
C2 = (C1 × V1) / V2 = (C1 × 1 mL) / 10 mL = C1 / 10After 5 serial steps: final dilution factor = 10⁻⁵ (1:100,000).
If a plate shows 150 colonies at dilution 10⁻⁵, the original count = 150 × 10⁵ = 1.5 × 10⁷ CFU/mL.
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Common Mistakes
1. Mixing volume units (mL vs L): Using V1 = 0.01 L and V2 = 100 mL in the same equation gives a 1000× error. Always convert to one unit first.
2. Confusing "final volume" with "volume of solvent added": C1V1 = C2V2 solves for the total final volume (V2), not the amount of water to add. Solvent added = V2 − V1.
3. Applying the formula to non-dilute solutions (activity ≠ concentration): For strong acids/bases above ~1 M, activity coefficients deviate from ideal; the simple C1V1 = C2V2 equation loses accuracy and thermodynamic activity must be considered.
4. Using incompatible concentration units: Mixing molarity (mol/L) with percent (g/100 mL) without converting first produces nonsensical results. Convert everything to the same unit before plugging into the formula.
5. Forgetting density corrections for percent w/w concentrations: Percent w/v (g per 100 mL) plugs directly into C1V1 = C2V2, but percent w/w (g per 100 g) requires a density conversion step first (e.g., 37% HCl w/w has density 1.19 g/mL → 12 M).
6. Assuming the formula applies to gases without correction: For gas-phase dilutions (e.g., ppm in air), temperature and pressure must be constant, or the ideal gas law must be applied alongside the dilution equation.
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Frequently asked questions
What do C1, V1, C2, and V2 actually represent?
C1 = initial (stock) concentration; V1 = volume of stock solution you will use; C2 = target (final) concentration; V2 = total final volume of the diluted solution. The formula states that the moles of solute before dilution (C1×V1) equal the moles after dilution (C2×V2), because adding solvent does not change the amount of solute — only its concentration.
Can I use this formula with percent (%) concentrations instead of molarity?
Yes — C1V1 = C2V2 is unit-agnostic as long as both concentrations use the same unit. Percent w/v (g/100 mL), mg/mL, ppm, ppb, and molarity (M) all work. For example, diluting 8.25% bleach to 0.5%: V1 = (0.5 × 1000) / 8.25 = 60.6 mL. The critical rule is that C1 and C2 must be in the same unit, and V1 and V2 must also share one unit.
What is a dilution factor and how does it relate to C1V1 = C2V2?
The dilution factor (DF) = C1/C2 = V2/V1. A 1:10 dilution means DF = 10 (you take 1 part stock and add 9 parts solvent, yielding 10 parts total). In C1V1 = C2V2 terms: if V1 = 1 mL and V2 = 10 mL, then C2 = C1 × (1/10). Serial dilutions of 1:10 repeated n times yield a final DF of 10ⁿ.
How do I calculate the volume of solvent (water) to add — not just the final volume?
C1V1 = C2V2 gives you V2, the total final volume. The volume of solvent to add is simply: Solvent added = V2 − V1. Example: diluting 10 mL of 1 M stock to 0.1 M → V2 = 100 mL → add 100 − 10 = 90 mL of water. Never pour V2 mL of water on top of V1 mL of stock, as the total volume would then be V1 + V2, not V2.
Does C1V1 = C2V2 work for serial dilutions in microbiology?
Yes. Each step of a serial dilution is a separate application of the formula. For a 1:10 dilution, you transfer 1 mL into 9 mL diluent: C2 = (C1 × 1 mL) / 10 mL = C1/10. After 5 steps, the cumulative dilution factor is 10⁻⁵. Colony count on a plate × dilution factor⁻¹ gives the original CFU/mL. NIST and the FDA Bacteriological Analytical Manual both use this serial dilution framework.
Is the formula accurate for concentrated acid or base solutions?
Only approximately. For dilute solutions (<0.1 M), C1V1 = C2V2 is highly accurate. For concentrated acids (e.g., 12 M HCl, 18 M H₂SO₄) or bases, the formula gives a useful first approximation, but thermodynamic activity coefficients deviate significantly from ideality, and heat of dilution must be managed safely. Always add concentrated acid to water slowly, never the reverse — an exothermic surge can cause spattering.
What bleach dilution does the CDC recommend for disinfection, and how do I calculate it?
The CDC recommends 1:10 dilution of household bleach (≈0.5% NaOCl) for general surface disinfection of non-porous surfaces. Using 8.25% bleach: V1 = (0.5% × 1000 mL) / 8.25% ≈ 60.6 mL bleach per liter of water. For food-contact surfaces, CDC recommends a 1:100 dilution (0.05–0.1% NaOCl). Reference: CDC Cleaning and Disinfection guidance.
Can this formula be used for IV drug dilutions in clinical settings?
Yes — it is routinely used in pharmacy and nursing. For example, to prepare 250 mL of a 2 mg/mL dopamine infusion from a 50 mg/mL vial: V1 = (2 mg/mL × 250 mL) / 50 mg/mL = 10 mL of the vial, added to 240 mL of NS or D5W. Always double-check with a pharmacist and institutional drug references; errors in drug dilution are a leading cause of medication adverse events per FDA MedWatch data.
What units can I use, and do I need to convert mL to L?
You do not need to convert mL to liters — as long as V1 and V2 use the same volume unit, the liters cancel algebraically. V1 = 10 mL, V2 = 100 mL with C1 = 1 M gives C2 = (1 × 10) / 100 = 0.1 M — identical to using 0.01 L and 0.1 L. Mixing units (e.g., V1 in mL, V2 in L) is a common and dangerous error; it introduces a 1000× factor into the result.
What is the difference between V2 (final volume) and the amount of solvent added?
V2 is the total final volume of the diluted solution, including both the original stock and the added solvent. The volume of solvent to add is V2 minus V1. Common mistake: pouring V2 mL of water directly onto V1 mL of stock — the resulting total volume would be V1 + V2, which is incorrect and produces a more dilute solution than intended.