Dilution Calculator
Calculate solution dilutions using C1V1 = C2V2. Find final volume, concentration, or solvent to add. Supports serial dilutions and multiple concentration units.
mL
Final Volume (V2)
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Solvent to Add —
Dilution Factor —
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mL
Final Volume V2 (mL)
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Solvent to Add (mL) —
Dilution Factor —
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µL
Dilution Summary
V2 (total final volume, mL) —
Solvent to Add (mL) —
Dilution Factor —
Per Tube (with dead volume)
Stock per Tube (µL) —
Solvent per Tube (µL) —
Total Volume Needed (with dead vol) —
How to Use This Calculator
- Enter the initial concentration (C1) and initial volume (V1) of your stock solution.
- Enter the desired final concentration (C2).
- The calculator shows final volume (V2) needed and how much solvent to add.
Formula
C1 × V1 = C2 × V2
V2 = (C1 × V1) / C2 | Solvent to add = V2 − V1 | Dilution factor = C1 / C2
Example
Example: Dilute 10 mL of 5 mol/L stock to 1 mol/L → V2 = (5 × 10) / 1 = 50 mL. Add 40 mL solvent.
Frequently Asked Questions
- The fundamental dilution equation is C1 × V1 = C2 × V2, where C1 is initial concentration, V1 is initial volume, C2 is final (diluted) concentration, and V2 is final total volume. This equation expresses conservation of moles: the number of moles of solute before dilution (C1 × V1) equals the number after (C2 × V2). Rearrange for any unknown: V2 = (C1 × V1) ÷ C2 (find final volume), V1 = (C2 × V2) ÷ C1 (find stock volume needed), C2 = (C1 × V1) ÷ V2 (find final concentration), or C1 = (C2 × V2) ÷ V1 (find original concentration).
- First calculate the final volume using V2 = (C1 × V1) ÷ C2. Then, the volume of solvent to add = V2 − V1. For example, to dilute 10 mL of 5 mol/L HCl stock to 1 mol/L: V2 = (5 × 10) ÷ 1 = 50 mL. Solvent to add = 50 − 10 = 40 mL of water. Important: always add acid to water (never water to concentrated acid) for safety. When mixing concentrated sulfuric acid with water, add the acid slowly to a large volume of cold water to prevent dangerous splashing from the exothermic reaction.
- A serial dilution is a sequence of equal dilution steps, where each step uses a portion of the previous step's diluted solution. It is used when the required dilution factor is too large to achieve in one step. For example, a 1:10 serial dilution repeated 5 times gives a total dilution factor of 10⁵ (100,000×). Each step: take 1 mL from the previous tube, add 9 mL solvent. After step 5, the original concentration has been reduced 100,000×. Serial dilutions are fundamental in microbiology (colony counting), pharmacology (dose-response curves), and analytical chemistry.
- The dilution factor (DF) is the ratio of the original concentration to the final concentration: DF = C1 ÷ C2 = V2 ÷ V1. A dilution factor of 10 means the solution is 10 times more dilute than the original. A 1:10 dilution = DF of 10. A 1:100 dilution = DF of 100. For serial dilutions, multiply the individual factors: three 1:10 dilutions = DF of 10 × 10 × 10 = 1,000. Final concentration after dilution: C2 = C1 ÷ DF. For example, diluting 2 mol/L by a factor of 20: C2 = 2 ÷ 20 = 0.1 mol/L.
- The C1V1 = C2V2 formula works with any consistent concentration unit — mol/L (molar, M), mmol/L (millimolar, mM), g/L, mg/mL, % (w/v or v/v), or ppm (parts per million). The key is to use the same units for both C1 and C2 — never mix mol/L with g/L without converting first. Volume units (V1 and V2) must also match — both in mL, both in L, etc. For example: diluting a 10% NaCl solution to 2%: (10% × V1) = (2% × V2). If V1 = 50 mL, V2 = 250 mL, add 200 mL of water.