# Dilution Calculator - C1V1=C2V2, Concentration Converter & Stock Acid Molarity

> Free dilution calculator: solve C1V1=C2V2, convert molarity, % w/w, ppm and molality, mix solutions, plan serial dilutions and dilute stock acids.

- URL: https://qilingtools.com/en/math/solution
- Category: Chemistry Tools (https://qilingtools.com/en/chemistry)
- Tags: [Chemistry](https://qilingtools.com/en/tags/chemistry)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Diluting a solution does not change the amount of solute, so C₁V₁ = C₂V₂. To make 500 mL of 1 M hydrochloric acid from 12 M stock, take V₁ = 1 × 500 / 12 ≈ 41.7 mL and make it up to 500 mL. The molarity of a concentrated reagent follows from its mass percent and density: c = 1000ρw / M, so 37% HCl (ρ = 1.19 g/mL) is about 12.08 M and 98% sulfuric acid (ρ = 1.84 g/mL) about 18.4 M. This calculator has five parts. The dilution tab solves for any one of C₁, V₁, C₂ or V₂ with concentrations in M, mM, μM or nM and volumes in L, mL or μL, and reports the dilution factor and the solvent to add. The converter takes a solute formula and solution density and converts between molarity, normality, mass percent (w/w), w/v percent, g/L, mg/L, ppm, ppb, molality and mole fraction. The mixing tab finds the concentration after combining two solutions of the same solute, or uses alligation to find how much of each to mix for a target. The serial dilution planner works from a dilution factor or a final concentration and lists the transfer volume, diluent volume and concentration of every tube. The stock tab includes typical grades of concentrated HCl, H₂SO₄, HNO₃, H₃PO₄, glacial acetic acid, HF, ammonia, 30% hydrogen peroxide and more, and tells you how much stock to measure for a target molarity and volume or a target mass percent and mass. All working is shown.

## How to use

1. Choose a tab: dilution, unit converter, mixing, serial dilution or concentrated stock
2. Enter the known values and units, or tap an example or a common reagent
3. Read the result and the working, then copy a value or the serial dilution table

## Features

- Solve C₁V₁ = C₂V₂ for any variable with M/mM/μM/nM and L/mL/μL
- Dilution factor and volume of solvent to add
- 10 concentration units: mol/L, N, w/w, w/v, g/L, mg/L, ppm, ppb, mol/kg and mole fraction
- Molar mass computed from the formula; custom solvent and equivalents
- Mix two solutions, or find volumes for a target concentration by alligation
- Serial dilution planner with per-tube concentration, total dilution, transfer and diluent volumes, copyable
- Reference table of 15 common concentrated acids, bases and ammonia with molarity
- Stock volume for a target molarity or mass percent, with acid dilution safety notes

## FAQ

### What is the molarity of 37% hydrochloric acid?

Use c = 1000ρw / M: 1000 × 1.19 × 0.37 / 36.46 ≈ 12.08 mol/L. In the same way 98% sulfuric acid (1.84 g/mL) is about 18.4 M, 65% nitric acid (1.40 g/mL) about 14.4 M and 28% ammonia (0.90 g/mL) about 14.8 M. Always check the actual assay and density on the bottle label.

### How do I use C1V1 = C2V2?

C₁ and V₁ are the stock concentration and the volume you take; C₂ and V₂ are the final concentration and the final total volume. Know any three and you get the fourth, as long as each quantity uses consistent units. To make 1 mL of 50 μM from a 10 mM stock, take V₁ = 50 μM × 1 mL / 10 mM = 5 μL and add diluent to 1 mL. V₂ is the total volume, not the volume of solvent added.

### How do I convert mass percent to molarity or ppm?

You need the solution density. Take 1 L of solution: its mass is 1000ρ g, the solute mass is 1000ρ × w, and molarity is that mass divided by the molar mass. ppm is a mass ratio (mg/kg); dilute aqueous solutions have ρ ≈ 1 g/mL, so 1 ppm ≈ 1 mg/L, but concentrated solutions need the density. Molality also needs the solvent mass, which is the solution mass minus the solute mass.

### How should I dilute concentrated sulfuric acid safely?

Dissolving sulfuric acid releases a lot of heat, so always add the acid slowly to water while stirring, never water to acid, or it can boil and spatter. Concentrated acids also contract when mixed with water, so let the solution cool and make it up to the mark in a volumetric flask instead of adding exactly V₂ − V₁ of water. Work in a fume hood with goggles and gloves.

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