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Concentration
Dilution Calculator

Find the final concentration after dilution. Enter stock concentration, volume taken, and total volume — get C₂ instantly with step-by-step calculation.

5
Calc Modes
0ms
Solve Time
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C₁ × V₁ = C₂ × V₂
Leave one field blank to solve for it. Keep C₁ & C₂ in the same units.
C₁ Stock Concentration (initial)
SOLVING
V₁ Stock Volume (to take)
SOLVING
C₂ Final Concentration (desired)
SOLVING
V₂ Final Volume (total)
SOLVING
DF = C₁ ÷ C₂ = V₂ ÷ V₁
Enter stock & final concentrations. Optionally add volume for a recipe.
C₁ Stock Concentration
C₂ Final Concentration (same unit)
Final Volume (optional — for mixing recipe)
Stock : Diluent → Volumes
Enter parts stock, parts diluent, and total volume to make.
Parts Stock (the "1" in 1:10)
Parts Diluent (the "10" in 1:10)
Final Volume (total)
V₁ = (C₂ × V₂) ÷ C₁
Dilute a % stock to a target % — works for w/v, v/v, and w/w.
Stock Strength (% — higher value)
%
Target Strength (% — desired)
%
Final Volume Needed (total to make)
Cₙ = C₀ ÷ DFⁿ
Build a multi-step serial dilution series with a consistent dilution factor.
Starting Concentration (C₀)
Dilution Factor per Step (e.g. 10 for 1:10)
Number of Steps (tubes after stock)
Concentration Unit (label, optional)
⚠️ Error message here
✅ Calculation Result
🧪 Overview

What Is a Concentration Dilution Calculator?

A concentration dilution calculator determines the final concentration (C₂) after diluting a stock solution. This is the most common dilution question: "I added X mL of Y concentration stock to Z mL total — what is the resulting concentration?" The tool applies C₂ = (C₁ × V₁) ÷ V₂ and supports molarity, mg/mL, ppm, and percentage units.

⚡

Benefits

  • Calculates C₂ directly from C₁, V₁, and V₂
  • Supports all common concentration units
  • Shows dilution factor alongside the result
  • Ideal for "what concentration did I make?" scenarios
🔬

Applications

  • Verifying concentration after preparing a solution
  • Back-calculating sample concentration from diluted readings
  • Environmental testing concentration determination
  • Quality control concentration verification

Concentration calculation after dilution is essential in analytical chemistry, where instrument readings on diluted samples must be multiplied by the dilution factor to obtain the original concentration. Environmental testing labs measuring water contaminants in ppm, clinical labs measuring analytes in mg/dL, and food labs measuring additives in µg/kg all use this concentration dilution calculator to convert between diluted and undiluted values.

📐 Core Equation

Concentration After Dilution

To find concentration after dilution, rearrange C₁V₁ = C₂V₂ to: C₂ = (C₁ × V₁) ÷ V₂. C₁ is what you started with, V₁ is how much you took, V₂ is the total volume after adding diluent, and C₂ is the resulting concentration.

Interactive: Hover each variable to see its role
C₁ × V₁ = C₂ × V₂
C₁ = High conc. V₁ = Small vol.
Stock Solution
+ Diluent
C₂ = Low conc. V₂ = Large vol.
Final Solution
💡 The total amount of solute (C × V) is the same in both vessels — only the concentration changes.

Rearrange the equation to solve for any unknown:

V₁ = (C₂ × V₂) ÷ C₁— how much stock to pipette
C₂ = (C₁ × V₁) ÷ V₂— what concentration you'll get
V₂ = (C₁ × V₁) ÷ C₂— total volume needed

This equation assumes ideal dilution — the solute does not change and volumes add linearly. For most aqueous solutions below 1 M, this assumption holds. The calculator also computes the dilution factor (DF = C₁/C₂) and the diluent volume (V₂ − V₁). These derived values complete the picture: concentration, factor, and recipe in one calculation.

🔢 Factor

Concentration and Dilution Factor

The dilution factor directly relates initial and final concentrations: C₂ = C₁ ÷ DF. If you know the dilution factor and the stock concentration, the final concentration follows immediately. A 10 mM stock diluted 100-fold gives 0.1 mM.

DF = C₁ ÷ C₂ = V₂ ÷ V₁

In clinical chemistry, automated analyzers report results at the "diluted" concentration. The technician enters the dilution factor, and the instrument automatically multiplies to report the original sample concentration. This concentration dilution calculator replicates that workflow — enter the diluted reading and the factor, and get the true sample concentration.

Interactive: Click a factor to see the stock-to-diluent ratio
1 part stock
1 part diluent
Factor2×
Stock1 part
Diluent1 part
Total2 parts
📋 Step by Step

Step-by-Step Concentration Dilution Calculator Guide

Follow these steps to calculate your dilution:

1
Record the stock concentration (C₁). Example: 5 M NaCl stock solution.
2
Record the volume of stock used (V₁). Example: 2 mL pipetted into a flask.
3
Record the total final volume (V₂). Example: 100 mL after adding water.
4
Calculate: C₂ = (C₁ × V₁) ÷ V₂. C₂ = (5 × 2) ÷ 100 = 0.1 M.
5
Verify the dilution factor. DF = 5 ÷ 0.1 = 50-fold ✓
🔬 Serial Dilution

Concentration at Each Serial Dilution Step

Tracking concentration through a serial dilution means applying C₂ = (C₁ × V₁) ÷ V₂ at each step, where the previous step's C₂ becomes the next step's C₁. Alternatively, use Cₙ = C₀ ÷ DFⁿ to jump directly to any step.

Cₙ = C₀ ÷ DFⁿ
C₀ = starting concentration · DF = dilution factor per step · n = step number
Interactive: Two-fold serial dilution from 1000 µM — hover each tube
Stock
1000 µM
1×
›
Tube 1
500 µM
2×
›
Tube 2
250 µM
4×
›
Tube 3
125 µM
8×
›
Tube 4
62.5 µM
16×
›
Tube 5
31.25 µM
32×
🧫 Each tube: Transfer a fixed volume → add diluent → mix → repeat. Concentration halves at every step.

Environmental testing laboratories measure contaminant concentrations in water, soil, and air samples. When concentrations exceed instrument range, technicians dilute and re-measure. The original concentration = measured concentration × dilution factor. EPA methods 524.2 (VOCs), 200.8 (metals by ICP-MS), and 524.4 require precise dilution factor tracking for regulatory compliance. This concentration dilution calculator ensures accurate back-calculation.

✏️ Worked Example

Concentration Dilution Calculator Example

Problem: A lab technician pipetted 0.5 mL of patient serum into 4.5 mL of diluent (1:10 dilution). The analyzer read 15 mg/dL for creatinine. What is the true concentration?

Step 1Identify variables
C₁ = ? mg/dL (true serum creatinine)
V₁ = 0.5 mL (serum volume)
V₂ = 5 mL (total: 0.5 + 4.5)
C₂ = 15 mg/dL (analyzer reading)
Step 2Rearrange formula
C₁ = C₂ × (V₂ ÷ V₁) = C₂ × DF
Step 3Substitute values
DF = 5 ÷ 0.5 = 10. C₁ = 15 × 10 = 150 mg/dL
Step 4Calculate diluent
True creatinine = 150 mg/dL
Step 5Verify
Critical value — notify physician immediately
Step 1 of 5
🧪
Recipe: The 1:10 dilution (0.5 mL serum + 4.5 mL saline) produced a 15 mg/dL reading. Multiplying by the dilution factor of 10 gives a true creatinine of 150 mg/dL — significantly above the reference range (0.7–1.3 mg/dL). Document the dilution factor in the LIS, flag as critical value, and notify the ordering physician per laboratory critical value policy. Re-run on undiluted sample if within analyzer linearity range to confirm.
❓ FAQ

Frequently Asked Questions

C₂ = (C₁ × V₁) ÷ V₂. Multiply the stock concentration by the stock volume, then divide by the total final volume. Example: 2 mL of 10 mM stock in 200 mL total → C₂ = (10 × 2) ÷ 200 = 0.1 mM. This concentration dilution calculator handles all units and shows the step-by-step calculation.

Multiply the measured concentration by the dilution factor. If you diluted 10-fold and measured 5 mg/L, the original = 5 × 10 = 50 mg/L. The dilution factor = total volume ÷ sample volume. For 1 mL sample + 9 mL diluent = 10 mL total: DF = 10/1 = 10. This back-calculation is essential in clinical chemistry, environmental testing, and food safety analysis.

M, mM, µM, nM, mg/mL, and percentage. Molarity (M, mM, µM, nM) for chemistry and biology. Mass/volume (mg/mL, µg/mL) for pharmacy and clinical applications. Percentage (% w/v, v/v) for industrial and household products. The calculator converts between molar prefixes automatically. For ppm, use mg/L which is equivalent for dilute aqueous solutions.