In short: to make a target concentration from a stronger stock, you need V1 = C2 × V2 / C1 of stock, topped up with water to your final volume. For a common example — 5.25% bleach diluted to a 200 ppm working solution — that's about 14.4 mL (roughly 1 tablespoon) per gallon of finished solution.
This is a dilution-arithmetic tool, not safety guidance. Always confirm the target concentration is appropriate for your use, and follow the product's label and safety data sheet.
How the calculation works
Every dilution follows the same rule: the amount of active ingredient doesn't change when you add water, only its concentration does. That's captured in the standard dilution equation, where C1 and V1 describe the stock and C2 and V2 describe the final, diluted batch:
C1 × V1 = C2 × V2
Rearranged for the stock volume you need: V1 = C2 × V2 / C1. The water to add is simply V2 − V1. If you need the more general case of solving for any one of the four values, the dilution calculator handles that directly.
Worked example. To make 1 gallon (3.785 L) of a 200 ppm solution from 5.25% (52,500 ppm) stock: V1 = 200 × 3.785 L / 52,500 = 0.01442 L, or 14.42 mL of stock. Water to add is 3.785 − 0.014 = 3.771 L (about 0.996 gal), and the dilution ratio is 1 part stock to about 261.5 parts water (1:262.5 total).
Stock needed at common target concentrations
Using 5.25% (52,500 ppm) stock to make 1 gallon of solution at each target concentration.
| Target concentration | Stock needed (mL) | Stock needed (tbsp) |
|---|---|---|
| 50 ppm | 3.61 | 0.24 |
| 100 ppm | 7.21 | 0.49 |
| 150 ppm | 10.82 | 0.73 |
| 200 ppm | 14.42 | 0.98 |
| 400 ppm | 28.84 | 1.95 |
| 600 ppm | 43.26 | 2.93 |
| 800 ppm | 57.68 | 3.90 |
Stock needed by strength, for a 200 ppm gallon
The stronger the stock, the less of it you need for the same target and batch size — 1 gallon at 200 ppm, across common strengths.
| Stock strength | Stock needed (mL) | Stock needed (tbsp) |
|---|---|---|
| 5.25% | 14.42 | 0.98 |
| 6% | 12.62 | 0.85 |
| 8.25% | 9.18 | 0.62 |
| 12.5% | 6.06 | 0.41 |
All figures computed from C1V1 = C2V2 using the 1% = 10,000 ppm convention; verify against your product's labeled strength before mixing.
Worked scenarios
Surface sanitizer, 1 gallon. 5.25% bleach diluted to a 200 ppm working solution: 14.42 mL stock (about 1 tablespoon) topped up with water to 1 gallon — a 1:261.5 dilution.
Food-contact quat sanitizer, 2 gallons. A 10% quaternary ammonium stock diluted to a 400 ppm working solution: 30.3 mL stock plus about 1.99 gal water — a 1:249 dilution (1:250 total).
Pool shock treatment, 5 gallons. 12.5% liquid chlorine diluted to an 800 ppm super-chlorination batch: 121 mL (about 0.032 gal) stock plus 4.97 gal water — a 1:155.3 dilution (1:156.3 total).
What else affects the result
Labeled strength can drift. Liquid chlorine bleach loses concentration over time, especially in heat or light — a bottle labeled 8.25% may be several percent weaker after months of storage. If the working concentration matters, verify it rather than trusting the printed strength alone.
Mixing order and safety. Add the concentrated stock into the water, not water into the stock, to reduce splashing and heat release with strong chemicals. Never mix bleach with ammonia or other cleaners. Follow the product's safety data sheet.
Density assumption. Converting between percent and ppm here assumes the solution's density is close to water (1 g/mL), which holds well for dilute aqueous stocks but is an approximation for viscous or dense concentrates. For related conversions, see the hardness ppm-to-gpg calculator or the conductivity-to-TDS calculator.
Frequently asked questions
What is a stock solution?
A stock solution is a concentrated liquid — a chemical, disinfectant or reagent — that you dilute with water to make a weaker working solution at the concentration you actually need. Buying or mixing one strong stock and diluting it on demand is usually cheaper and more consistent than buying many pre-diluted products.
What formula does this calculator use?
It uses the standard dilution equation C1V1 = C2V2, where C1 and V1 are the concentration and volume of the stock solution, and C2 and V2 are the concentration and volume of the final, diluted solution. Solving for V1 gives the stock volume needed; subtracting V1 from V2 gives the water to add.
How does the calculator convert between percent and ppm?
It uses the standard aqueous-solution convention that 1% (weight/volume) equals 10,000 ppm, which assumes the solution's density is close to water. This holds well for dilute chemical solutions like bleach or sanitizer stocks, but is an approximation for dense concentrates.
Why does it say the target concentration is impossible?
This calculator only dilutes a stock down to a weaker concentration. If your target concentration is equal to or higher than the stock concentration, there is no volume of stock and water that produces it — you would need a stronger stock instead.
Does it matter if I add stock to water or water to stock?
The calculated volumes are the same either way, but for strong acids and concentrated chemicals, safe practice is generally to add the concentrated stock into the water, not the reverse, to limit splashing and heat release. Always follow the product's own safety data sheet.
Can I use this to prepare drinking water disinfection doses?
This tool only performs the dilution arithmetic; it does not verify that a resulting concentration is safe or appropriate for a specific use such as drinking water. For potable water disinfection, follow your local health authority's or water utility's published guidance rather than a target concentration you set yourself.
Sources & references
- American Public Health Association (APHA). Standard Methods for the Examination of Water and Wastewater.
- U.S. Environmental Protection Agency (EPA). Guidance on selecting and using disinfectants for water treatment.
- Centers for Disease Control and Prevention (CDC). Guidance on preparing diluted bleach solutions.
Sarah Bennett, MS
Water Quality & Sustainability Specialist · Portland, Oregon
Environmental scientist (MS, Water Resources) with 9+ years in residential water quality, treatment, and usage efficiency, and 150+ completed assessments. Sarah writes and reviews the treatment, usage, and cost calculators on watercalculator.us. Read full bio
MS Environmental Science, Water Resources (2018) · BS Environmental Engineering (2016)