稀释计算器 — C₁V₁=C₂V₂ 溶液稀释
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.
常见问题
稀释计算器是如何工作的？
稀释计算器使用稀释公式 C₁V₁ = C₂V₂，其中 C₁ 是初始浓度，V₁ 是初始体积，C₂ 是目标浓度，V₂ 是最终体积。输入任意三个值，即可计算第四个未知值。
什么是稀释因子？
稀释因子是溶液被稀释的倍数，等于最终体积除以初始体积（V₂/V₁）。例如，1:10 的稀释因子表示 1 份原液加 9 份溶剂，最终浓度为原来的 1/10。
我需要加多少溶剂？
需要加入的溶剂量 = 最终体积（V₂）减去初始体积（V₁）。计算器会在给出最终体积的同时，也显示需要添加的溶剂量。
我可以用于哪些单位？
该计算器支持各种体积单位（mL、L、μL）和浓度单位（mol/L、mg/mL、%、ppm 等）。只需确保同一计算中浓度单位保持一致即可。
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.