Percent Solution Dilution Calculator: Formula, Table and Examples

To dilute a percent solution, use C₁ × V₁ = C₂ × V₂: the volume of stock you need is V₁ = C₂ × V₂ ÷ C₁, where both strengths are written on the same basis (both w/v or both v/v). You then add diluent to bring the mixture up to the final volume V₂. This page gives the formula, a printable lookup table, two worked examples and code you can paste into a spreadsheet or script.

The dilution formula for percent solutions

The dilution equation holds because the amount of solute does not change when you add diluent. Written for percent strengths:

• C₁ = strength of the stock (%)
• V₁ = volume of stock to take (mL)
• C₂ = strength you want (%)
• V₂ = final volume you want (mL)

V₁ = C₂ × V₂ ÷ C₁, and the dilution factor is DF = C₁ ÷ C₂, so V₁ = V₂ ÷ DF. Volumes may be in any unit as long as V₁ and V₂ use the same one.

Two points keep the arithmetic honest. First, “make up to V₂” means add diluent until the mixture reaches the final volume mark; do not simply add V₂ − V₁ of diluent, because the volumes of some liquid mixtures are not exactly additive. Second, the stock and the target must share a basis, as explained below.

w/v, v/v and w/w: do not mix bases

Laboratory labels use three conventional shorthands:

• % w/v: grams of solute per 100 mL of solution, so 1 % w/v = 10 g/L.
• % v/v: millilitres of solute per 100 mL of solution.
• % w/w: grams of solute per 100 g of solution (see mass percent solution).

The formula is valid only when C₁ and C₂ are on the same basis. A w/v stock cannot be diluted to a v/v target by this equation.

The NIST Guide for the Use of the SI (SP 811, chapter 7, section 7.10.2) says the symbol % represents simply a number and that attaching qualifiers to it, such as “% (m/m)” or “% (V/V)”, should be avoided; it recommends stating the quantity in words instead, for example “the mass fraction is 10 %”. Lab labels still use w/v and v/v widely, so in a protocol write the basis in words (“10 % weight per volume, 100 g/L”) and convert to g/L (multiply % w/v by 10) when a method is ambiguous.

Lookup table: mL of stock per 100 mL of final solution

Each cell is the volume of stock to measure, in millilitres, so that topping up to 100 mL gives the target strength. It equals target ÷ stock × 100, rounded to 0.1 mL. “No dilution” means the target equals the stock, so use it as is. A dash means the target is stronger than the stock and cannot be reached by dilution. For other final volumes, scale the cell: for 500 mL multiply by 5, for 1 L by 10. Use unrounded values from the formula if the rounding matters for your work.

Stock strength (%)	1 % final	2 % final	5 % final	10 % final	20 % final	50 % final
100 %	1.0	2.0	5.0	10.0	20.0	50.0
70 %	1.4	2.9	7.1	14.3	28.6	71.4
50 %	2.0	4.0	10.0	20.0	40.0	no dilution
30 %	3.3	6.7	16.7	33.3	66.7	–
20 %	5.0	10.0	25.0	50.0	no dilution	–
10 %	10.0	20.0	50.0	no dilution	–	–

Table source: calculated from the dilution equation above; every cell was generated by script and rounded to one decimal place.

Worked example 1: diluting a w/v stock

You have a 20 % w/v stock and need 500 mL of 5 % w/v.

1. V₁ = C₂ × V₂ ÷ C₁ = 5 × 500 ÷ 20 = 125 mL of stock.
2. Dilution factor = 20 ÷ 5 = 4, and 500 ÷ 4 = 125 mL, which agrees.
3. Check the solute: 5 % w/v is 5 g per 100 mL, so 500 mL holds 25 g; 125 mL of 20 % w/v stock holds 125 × 0.20 = 25 g.
4. Measure 125 mL of stock into a graduated vessel and add diluent up to the 500 mL mark.

The same answer appears in the table: 5 % from a 20 % stock is 25.0 mL per 100 mL, and 25.0 × 5 = 125 mL.

Worked example 2: a v/v stock

You have a 70 % v/v stock and need 500 mL of 10 % v/v.

1. V₁ = 10 × 500 ÷ 70 = 71.43, rounded to 71.4 mL of stock.
2. Dilution factor = 70 ÷ 10 = 7, and 500 ÷ 7 = 71.4 mL.
3. Add diluent until the total volume reaches the 500 mL mark; top up to the mark rather than relying on a diluent volume found by subtraction.

The table gives 14.3 mL per 100 mL for this pair, and 14.3 × 5 = 71.5 mL, which differs slightly from 71.4 mL only because the table cell is rounded first. For critical work calculate from the formula.

Compute it in Excel, R or Python

Excel or Google Sheets (stock % in A2, target % in B2, final volume in C2):

=B2*C2/A2

R:

v1 <- function(c1, c2, v2) c2 * v2 / c1
v1(20, 5, 500)   # 125

Python:

def stock_volume(c1, c2, v2):
    if c2 > c1:
        raise ValueError("target is stronger than stock")
    return c2 * v2 / c1

print(round(stock_volume(70, 10, 500), 1))  # 71.4

Safety: read the SDS of the stock first

Before diluting, read the safety data sheet (SDS) for the concentrated stock, because the hazards of the solution you are handling are those of the stock. Under the US OSHA Hazard Communication Standard (29 CFR 1910.1200), an SDS has 16 sections in a fixed order; the ones most useful before a dilution are Section 2 (hazard identification), Section 7 (handling and storage) and Section 8 (exposure controls and personal protection). For laboratories, paragraph (b)(3)(ii) requires employers to maintain the SDSs received with incoming shipments of hazardous chemicals and keep them readily accessible to laboratory employees in their work areas during each work shift. For how hazard classes and labels are defined, see GHS classification of chemicals. Follow your institution’s chemical hygiene plan for protective equipment and waste.

Related guides

• Converting percent to molarity: molarity and solution calculations
• Large dilution factors: serial dilution technique
• Making working solutions: buffer and solution preparation
• Measuring small volumes: what is a pipette

FAQ

How do I dilute a 10 % solution to 1 %?

The dilution factor is 10, so take 1 part stock and make up to 10 parts total. For 100 mL of final solution, that is 10 mL of stock made up to 100 mL.

Does C1V1 = C2V2 work with percent concentrations?

Yes, provided both strengths use the same basis (w/v with w/v, v/v with v/v) and both volumes use the same unit.

How many grams are in a 1 % w/v solution?

1 % w/v is 1 g per 100 mL, which is 10 g per litre.

What if my target is stronger than my stock?

Dilution cannot raise strength. You need a stronger stock or must dissolve more solute.

Sources

• NIST SP 811, chapter 7: Rules and style conventions for expressing values of quantities (checked 2026-10-29)
• 29 CFR 1910.1200, Hazard Communication (checked 2026-10-29)