Titration is how chemists measure a concentration they do not know by using a concentration they do know. You put a measured volume of the unknown solution in a flask, add an indicator, and drip in a standard solution from a burette until the colour changes. The volume you used, the titre, tells you how many moles reacted, and from that you work out the unknown concentration. This calculator does the final step of that chain.
The maths is a chain of moles. Moles of titrant equal its concentration times its volume in litres. At the endpoint, the moles of analyte follow from the balanced equation: if one mole of titrant reacts with one mole of analyte, the moles are equal. Divide those moles by the analyte volume in litres, and you get the unknown concentration. The tool adds one more input, the mole ratio, for reactions where the ratio is not one to one.
Here is a worked example. You titrate 20 millilitres of an unknown acid with 0.1 molar sodium hydroxide, and the endpoint comes at 25 millilitres. The moles of base are 0.1 times 0.025 litres, which is 0.0025 moles. With a one-to-one ratio, the acid also has 0.0025 moles in 20 millilitres, so its concentration is 0.0025 divided by 0.020, which is 0.125 molar. The tool returns 0.1250 molar and the moles used, so you can follow both steps.
The mole ratio is where students lose marks. Sulfuric acid, H2SO4, gives two hydrogen ions, so it needs two moles of sodium hydroxide per mole of acid. In that case the ratio input is 2 for titrant per analyte only if you define it that way, so read the tool label: it asks for titrant moles per one analyte mole. If the equation says one acid reacts with two bases, enter 2, and the tool divides the titrant moles by 2 before dividing by the analyte volume. Always write the balanced equation first.
A single titre is never enough for a good result. Real titration work repeats the titration until two or three titres agree within about 0.1 millilitres, and then averages the agreeing values. A first rough titration finds the endpoint region, and later careful titrations approach it drop by drop. If your titres scatter widely, something is off: a dirty burette, a wrong indicator, or an endpoint read too late. The calculator cannot see those problems, so it trusts the number you type.
Indicators deserve a note, because the endpoint is a colour judgement, not a machine reading. Phenolphthalein turns pink in base, methyl orange turns yellow, and each indicator changes over a different pH range. The right indicator is the one whose change matches the pH at the equivalence point of your reaction. Using the wrong indicator shifts the endpoint and the titre, and no calculation can fix a titre measured at the wrong colour change.
Use this calculator as a practice aid for study and homework, not as lab procedure. It is an educational estimator, and a real titration follows a written protocol, a supervisor, and safety rules for the acids, bases, and indicators involved. Some of these chemicals burn skin and eyes, and burettes need training to read and handle. Check every result against your class notes and a worked example, and never run a real titration from a web tool alone.
Back titration rescues samples that react slowly or have no sharp endpoint of their own. You add a known excess of a reagent, let the slow reaction finish, and then titrate what is left over with a second standard solution. The difference between what you added and what remains is what the sample consumed, and from that difference you calculate the sample, exactly as in a direct titration. Blank runs matter just as much: titrating a sample with nothing in it shows how much titrant the procedure itself consumes, and that blank value is subtracted before any calculation. Skipping the blank is a common reason student results run a little high.