Molarity and Dilution Calculator
Calculate the final molarity after diluting a stock solution (M2 = M1·V1/V2), or the volume of stock you need to reach a target molarity (V1 = M2·V2/M1). Perfect for preparing working solutions in the lab.
Last updated: September 2026
Formula below · 2 sources (pubchem.ncbi.nlm.nih.gov, Wikipedia) · Updated Sep 2026
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About this calculator
The dilution equation is derived from conservation of moles of solute: moles before = moles after, so M1 × V1 = M2 × V2. Adding solvent changes the volume but not the amount of solute. This calculator solves it two ways. 'Find Final Molarity' returns M2 = (M1 × V1) / V2 from the stock molarity, the volume of stock taken and the final volume. 'Find Required Initial Volume' returns V1 = (M2 × V2) / M1 — how much stock to measure out to make V2 of a solution at the target molarity M2. Volumes are in mL (any unit works if V1 and V2 match). The target molarity must be below the stock molarity, since dilution can only lower concentration. Molarity itself is defined as moles of solute divided by liters of solution (n / V), making it the most common concentration unit in quantitative analytical and synthetic chemistry.
How to use
Example 1 — Find Final Molarity. You have a 10 M HCl stock. You take V1 = 50 mL and dilute to V2 = 500 mL with water. M2 = (M1 × V1) / V2 = (10 × 50) / 500 = 1.0 M. Enter M1 = 10, V1 = 50, V2 = 500, choose 'Find Final Molarity', and the calculator returns 1.0 M — a standard 1-in-10 dilution. Example 2 — Find Required Initial Volume. You need 250 mL of 1.0 M solution from a 2.5 M stock. Choose 'Find Required Initial Volume' and enter M1 = 2.5, V2 = 250 and target M2 = 1.0 (the V1 field is ignored in this mode). V1 = (1.0 × 250) / 2.5 = 100 mL: measure 100 mL of stock and make it up to 250 mL. Always add acid to water, not water to acid.
Frequently asked questions
What is the standard dilution formula M1V1 equals M2V2 and when does it apply?
M1V1 = M2V2 states that the number of moles of solute before dilution equals the number after: molarity times volume is constant. It applies whenever the solvent added is ideal (pure water, density-matched, no reaction with solute) and the volumes are additive. The formula is the starting point for all serial dilution calculations in microbiology, pharmacology, and analytical chemistry. Deviations occur with concentrated acids or highly ionic solutions where volume contraction on mixing makes the final volume slightly less than V1 + added solvent.
How do I calculate how much stock solution I need?
Choose 'Find Required Initial Volume' and enter the stock molarity (M1), the final volume you want (V2) and the target molarity (M2). The calculator rearranges M1V1 = M2V2 to V1 = M2·V2/M1. For example, 500 mL of 0.1 M NaOH from a 2 M stock needs V1 = 0.1 × 500 / 2 = 25 mL of stock, made up to 500 mL in a volumetric flask. If the diluent is not water (ethanol, DMSO, acetonitrile), the moles of solute are still conserved, so the same equation applies as long as you measure the final total volume; non-additive mixing volumes are handled by filling to the mark rather than by a correction factor.
How many significant figures should I use when reporting diluted molarity values?
Report your final molarity to the same number of significant figures as your least precise input. Volumetric glassware (Class A burettes, pipettes) is typically accurate to 3–4 significant figures, while graduated cylinders give only 2–3. If your stock solution molarity is known to ±0.5%, carry three significant figures throughout. Avoid false precision — writing 1.0000 M when your volumes were measured to ±1 mL in 100 mL (1% error) implies more certainty than the experiment warrants.