C1V1=C2V2 Calculator Calculators

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The dilution formula C1V1 = C2V2 states that the initial concentration (C1) multiplied by the initial volume (V1) equals the final concentration (C2) multiplied by the final volume (V2). It is based on conservation of moles: the number of moles of solute doesn't change when you add solvent. Use it to find: the volume of stock solution to take (V1), the final concentration (C2), or the initial volume needed. Units must be consistent on both sides. V2 is the total final volume — not the volume of diluent added.

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Formula and Rearrangements

C1 × V1 = C2 × V2

  • Find V1 (volume of stock): V1 = C2 × V2 / C1
  • Find C2 (final concentration): C2 = C1 × V1 / V2
  • Find V2 (total final volume): V2 = C1 × V1 / C2

Example: prepare 250 mL of 0.1 M NaCl from 2.0 M stock: V1 = (0.1 × 250) / 2.0 = 12.5 mL. Take 12.5 mL of stock; add water to 250 mL.

Common Mistakes

  • V2 = total volume, NOT volume of water added (water added = V2 − V1)
  • Units must match: if C in M, V in mL on both sides
  • Never apply to mixing two different solutes

Serial Dilutions

Apply C1V1 = C2V2 at each step. Each 1:10 dilution reduces concentration by 10×: C_n = C₀ × (1/dilution factor)^n. Example: 1 mg/mL → 1:10 × 3 steps → 0.001 mg/mL (1 μg/mL).

Glossary

C1V1 = C2V2
The dilution formula; V1 = C2×V2/C1; calculates volume of stock needed for any working concentration; based on conservation of moles; units must be consistent within each variable pair.
Serial Dilution
Sequential application of C1V1 = C2V2; each step reduces concentration by the dilution factor; C_n = C₀ × (dilution factor)^n; used in microbiology, pharmacology, and standard curve preparation.
Dilution Factor (DF)
V2/V1 = C1/C2; the factor by which concentration is reduced; 1:10 dilution = DF of 10; multiply final concentration by DF to recover original concentration.

Frequently Asked Questions

V1 (stock volume needed) = C2 × V2 / C1. Steps: identify which value is unknown; plug in the three known values; solve. Example 1: prepare 100 mL of 0.5 M glucose from 5.0 M stock: V1 = (0.5 × 100)/5.0 = 10 mL. Transfer 10 mL of 5.0 M stock to a 100 mL volumetric flask; add water to 100 mL. Example 2: dilute 20 mL of 0.8 M HCl with 60 mL water: V2 = 20 + 60 = 80 mL. C2 = (0.8 × 20)/80 = 0.2 M. Note: V2 = total volume, not just diluent!

Units must be consistent on both sides: C1 and C2 must use the same concentration unit (both in M, both in mg/mL, both in %, both in μg/μL, etc.). V1 and V2 must use the same volume unit (both in mL, both in μL, both in L, etc.). C and V don't need to be in compatible SI units with each other — only within each pair. Example (mixing units): C1 = 1 mM; V1 = 50 μL; C2 = 0.01 mM; V2 = ? V2 = (1 × 50)/0.01 = 5,000 μL = 5 mL. The formula works regardless of unit — as long as C1 and C2 are the same units and V1 and V2 are the same units.

A serial dilution applies C1V1 = C2V2 repeatedly. At each step: the previous diluted solution becomes C1; the transfer volume is V1; the new tube total volume is V2; C2 = C1 × V1/V2. For a 1:10 serial dilution (transfer 1 mL into 9 mL diluent): C2 = C1 × 1/10 each step. After n steps: C_n = C₀ × (1/10)^n. Example: start at 10⁶ CFU/mL. After step 1: 10⁵. After step 2: 10⁴. After step 3: 10³. Plate 0.1 mL of step 3 → expected 100 colonies (10³ × 0.1 = 100 CFU) → in the 30–300 counting range.

Dilution ratio: the ratio of solute volume to total solution volume (1:10 means 1 part sample + 9 parts diluent = 10 parts total). Dilution factor (DF): the inverse of the dilution ratio; DF = V2/V1 = 10 for a 1:10 dilution; multiply DF × final count to get original concentration. Fold dilution: how many times more dilute the final solution is; 10-fold dilution = 1:10. Example: plate count = 85 colonies; 0.1 mL of 10⁻⁵ dilution plated: DF = 10⁻⁵ × 0.1 = 10⁻⁶. CFU/mL original = 85 / 10⁻⁶ = 85 × 10⁶ = 8.5 × 10⁷ CFU/mL.