Dilution Calculator — C₁V₁=C₂V₂ Solution Dilution
Use the dilution formula C₁V₁ = C₂V₂ to solve for any unknown in a dilution problem. Enter three of the four values — initial concentration (C₁), initial volume (V₁), final concentration (C₂), or final volume (V₂) — and this calculator instantly computes the missing value. It also shows the volume of solvent to add (V₂ − V₁). Supports M, mM, % concentration units and L, mL, μL volume units.
Dilution Calculator — C₁V₁ = C₂V₂
Leave one field blank to solve for it. Fill in the other three.
Frequently Asked Questions
What is the dilution formula C1V1 = C2V2?
C1V1 = C2V2 is the fundamental dilution equation where C1 is the initial (stock) concentration, V1 is the initial volume taken from the stock, C2 is the final (working) concentration, and V2 is the final total volume after dilution. It works because the number of moles of solute is conserved: you are only adding solvent, not more solute. Any consistent unit pair can be used — M and mL, % and L, etc. — as long as C1 and C2 share a unit and V1 and V2 share a unit.
How do I calculate how much stock solution I need?
Rearrange the formula to V1 = (C2 × V2) / C1. For example, to prepare 500 mL of a 0.1 M solution from a 5 M stock: V1 = (0.1 × 500) / 5 = 10 mL. Take 10 mL of the stock solution, then add enough solvent (usually water) to bring the total volume to 500 mL.
How much solvent do I need to add?
The volume of solvent to add equals V2 − V1 (final volume minus the volume of stock solution used). For instance, if you need V1 = 10 mL of stock to make V2 = 500 mL of working solution, you add 500 − 10 = 490 mL of solvent. This calculator shows the 'Solvent to add' value automatically.
What is a dilution factor?
The dilution factor (DF) is the ratio of the final volume to the initial volume: DF = V2 / V1. It tells you how many times more dilute the final solution is compared to the stock. A 1:10 dilution means V2/V1 = 10, so the final concentration is 1/10 of the original. Equivalently, DF = C1 / C2.
What is a serial dilution?
A serial dilution is a sequence of stepwise dilutions where each diluted solution becomes the stock for the next step. It is used when a single dilution step would require impractically small volumes. For example, a 1:1,000,000 dilution can be achieved as six 1:10 steps in series. The total dilution factor equals the product of all individual dilution factors.
Can I use this calculator for any concentration unit?
Yes. The C1V1 = C2V2 equation is unit-agnostic as long as you use the same concentration unit for C1 and C2, and the same volume unit for V1 and V2. You can use molar (M), millimolar (mM), percent (%), mg/mL, ng/μL, or any other concentration unit. The calculator displays M, mM, and % as label options for your reference, but the math is identical regardless of the unit selected.
What does 'diluting to' vs 'diluting by' mean?
These phrases describe dilution in two different ways. 'Diluting to 1:10' means the final solution is 10 times less concentrated than the stock (V2/V1 = 10, or C2 = C1/10). 'Diluting by 1:10' sometimes means the same, but in some contexts it means you add 10 parts solvent for every 1 part stock, making the total 11 parts (C2 = C1/11). Always clarify which convention is meant in your protocol.
How is dilution used in laboratory practice?
Dilution is used throughout the lab: preparing working solutions from concentrated stocks, reducing sample concentration before spectrophotometric measurement, making calibration standards, preparing microbial plating suspensions for colony counting, and titrating reagents. The C1V1 = C2V2 formula is the foundation for all solution preparation calculations in chemistry, biochemistry, microbiology, and clinical diagnostics.
Dilution Equation
Dilution is the process of reducing the concentration of a solution by adding solvent. The fundamental relationship governing all dilutions is the dilution equation C₁V₁ = C₂V₂, which states that the number of moles of solute is conserved when you dilute a solution. This calculator solves for any one of the four variables when the other three are known.
The C₁V₁ = C₂V₂ Formula
C₁V₁ = C₂V₂
All four variables must use consistent units. Concentration can be in M, mM, %, or any other unit — as long as C₁ and C₂ use the same unit. Likewise V₁ and V₂ must share a unit (L, mL, μL, etc.).
Rearranged forms:
- C₁ = (C₂ × V₂) / V₁ — solve for initial concentration
- V₁ = (C₂ × V₂) / C₁ — solve for initial volume (stock volume needed)
- C₂ = (C₁ × V₁) / V₂ — solve for final concentration
- V₂ = (C₁ × V₁) / C₂ — solve for final volume
Step-by-Step Example
Problem: You have a 10 M stock solution of NaCl. How much stock solution do you need to prepare 500 mL of a 0.5 M working solution?
Given: C₁ = 10 M, C₂ = 0.5 M, V₂ = 500 mL
Find: V₁ (volume of stock to use)
V₁ = (C₂ × V₂) / C₁
V₁ = (0.5 × 500) / 10
V₁ = 250 / 10 = 25 mL
Take 25 mL of the 10 M stock, then add solvent (water) to bring the total volume to 500 mL. Solvent to add = 500 − 25 = 475 mL.
How to Make a Dilution
- Calculate how much stock solution you need using V₁ = (C₂ × V₂) / C₁.
- Pipette the calculated volume (V₁) of stock into a clean volumetric flask or container.
- Add solvent (usually distilled water) slowly while mixing, until the total volume reaches V₂.
- Always add concentrated solution to solvent, not the other way around — especially for acids (exothermic mixing).
- Mix thoroughly and label the container with the new concentration, date, and preparer.
Serial Dilutions
A serial dilution is a series of stepwise dilutions, each using the previous dilution as the new stock. Serial dilutions are used when the required dilution factor is very large (e.g., 1:10,000 or greater), making a single-step dilution impractical.
Example: 1:1000 dilution via three 1:10 steps
Step 1: 1 mL stock + 9 mL water → 10 mL at 1/10 concentration
Step 2: 1 mL of Step 1 + 9 mL water → 10 mL at 1/100 concentration
Step 3: 1 mL of Step 2 + 9 mL water → 10 mL at 1/1000 concentration
The total dilution factor equals the product of all individual dilution factors: 10 × 10 × 10 = 1000.
Common Lab Dilutions
Quick reference for frequently used dilution scenarios in biology, chemistry, and clinical labs.
| Dilution | Dilution Factor | Example Use |
|---|---|---|
| 1:2 | 0.5× | Halving a reagent for duplicate assays |
| 1:5 | 0.2× | Diluting a 5 M stock to 1 M |
| 1:10 | 0.1× | Serial dilution base step; blood counts |
| 1:100 | 0.01× | Antibody dilutions; urine samples |
| 1:1,000 | 0.001× | Primary antibody dilutions in Western blots |
| 1:10,000 | 0.0001× | Secondary antibody dilutions; ELISA |
| 1:1,000,000 | 1×10⁻⁶ | Bacterial colony counts; environmental samples |
Related Tools
- Molarity Calculator — Solve for molarity (M), moles (n), or volume (V) using M = n/V. Includes mass-to-moles helper with common compound presets.
- mEq to mg Calculator — Convert between milliequivalents and milligrams for electrolytes and ionic compounds.