Math

Evaluate scientific expressions with reproducible calculation steps and validation receipts.

Enter a fraction expression such as 2 3/4 ÷ 2/3. Get the exact reduced answer, mixed number, decimal, visual model, step-by-step explanation and a reproducible verification.

Calculate a logarithm in any valid base, or solve the same equation for the argument or base. See the working, verify the result and explore it on a graph.

One calculator for every common percentage question: percent of a number, percentage change, increase and decrease, percentage difference, reverse percentages, points versus percent, discounts, compound changes and conversions — each answer with its formula, working and interpretation.

Solve ax² + bx + c = 0 from coefficients or by typing the whole equation. You get the discriminant, exact roots in simplified radical or complex form, decimals to your chosen precision, every solving step, the vertex and parabola properties, equivalent forms, a graph and an independently verified calculation receipt.

Enter any number — a plain decimal, E notation, 6.022 × 10²³ or a non-normalized form like 53 × 10⁵ — and get the scientific, standard, E and engineering forms at once, with the exponent explained.

Count the significant figures in any number, round to any number of sig figs, or run a whole calculation and see which input limited the answer.

Calculate a confidence interval for a mean, a proportion, a difference between two groups, a paired difference, a standard deviation, a correlation or an event rate — with the recommended method chosen for you, the formula substituted with your own numbers, every step shown and the critical value independently verified.

Calculate the sample or population standard deviation of a data set — together with the variance, mean, range and standard error — with every step shown, every observation’s contribution tabulated, and the result verified by a second, independent algorithm.

Calculate the area of a shape, room, irregular polygon, property or 3D solid. Choose what you are measuring, enter the dimensions in any supported units, and see the formula, substitution, conversions and verification.

Use the volume calculator to find the volume of common 3D shapes, containers, tanks and pipes. Choose a shape, enter its dimensions in any supported units, and see the formula, calculation steps and converted result.

A cubic centimetre is exactly a millilitre — not approximately, by definition — so "cc to grams" is the same question as "mL to grams" wearing older clothes. One cc of water is 0.998 grams at room temperature. One cc of honey is 1.43 grams. The unit persists in two places that rarely talk to each other: clinical notes, where syringes and drains are measured in cc, and engines, where displacement is quoted in cc. Both mean the same volume.

Convert metric, US customary, Imperial and scientific units, see the conversion formula, and verify the definition behind every result.

A thousand grams of water is 1.0018 litres at room temperature, not one litre exactly. The coincidence that makes people expect 1 is real but narrow: the kilogram was originally defined as the mass of a litre of water, and water at 4 °C still hits 0.99997 g/mL. Twenty degrees later it is 0.99820, and the litre has grown by two parts in a thousand. For anything that is not water the coincidence disappears entirely. A thousand grams of honey is 0.699 litres. Of olive oil, 1.095.

A gram is a thousand milligrams, exactly, because that is what the prefix means. The conversion is a decimal point moved three places — the interesting part is the questions that look like this one and are not.

An ounce is 28.349523125 grams, exactly. That handles every grams-to-ounces question where both sides are a mass — and none of the ones where somebody means fluid ounces, which is a volume and a different problem entirely.

Grams and pounds are both masses, so the conversion between them is a single exact number and nothing else: one pound is 453.59237 grams by definition. Set the value, read it either way, and see the same mass in every other unit underneath.

A period is one divided by a frequency, which means this conversion is a curve rather than a scale. 1 Hz is 1000 ms, 10 Hz is 100 ms, 100 Hz is 10 ms — every tenfold rise in frequency divides the period by ten.

A kilogram of water fills 0.2646 US gallons. A kilogram of honey fills 0.1847 — thirty percent less, for the same mass. This pairing shows up wherever something is bought by weight and stored or shipped by volume: chemicals, fuels, food ingredients in bulk. In all of those the density is a known property of the product, usually printed on the safety data sheet. The trouble is that a converter which does not ask will use water's, and water is one of the denser ordinary liquids.

4.5 kilograms is 9 pounds 14.7 ounces. Neither half of that is an answer on its own: 9 lb is wrong, and 158.7 oz is right and useless, because nobody describes a weight that way. That pairing is the whole reason this page is separate from an ordinary unit converter. A tool that returns 9.92 lb has answered a different question from the one that was asked.

A kilogram is a million milligrams. Both units are SI, so this is not a conversion factor anyone measured — it is two prefixes multiplying, and the answer is a decimal point moved six places.

One kilogram is 2.2046226218 pounds. The factor looks like a measurement and is not: it falls out of the pound being defined as exactly 453.59237 grams, which is why it runs on for as many digits as you care to print.

"How many ounces in a litre" has two correct answers and they are not close. If you mean fluid ounces, a litre is 33.814 of them and the substance is irrelevant — it is a pure volume conversion. If you mean ounces of weight, a litre of water is 35.2 ounces, a litre of olive oil 32.2, and a litre of honey 50.4. This page answers the weight question, because that is the one that needs a density. If you wanted the volume one, the number is 33.814 and nothing else enters it.

A litre of water weighs 2.20 pounds. A litre of olive oil weighs 2.01. A litre of honey weighs 3.15. The question "how many pounds in a litre" has one answer per substance and a 57 percent spread between the lightest and heaviest thing this page carries. The pairing itself is a clue that something metric is being weighed for something imperial — shipping, freight, a recipe crossing an ocean — and in all three cases the substance is known to whoever is asking. It just is not in the search box.

1 mg/dL is 10 µg/mL. mg/dL is how most clinical chemistry is reported in the United States; µg/mL is how a laboratory method describes the same concentration. The factor between them is ten.

1 mg/L is 1000 µg/L. The litre is the same on both sides, so only the mass prefix moves. Regulatory limits are written in whichever of the two keeps the number readable, which is why the same substance appears in both across different documents.

1 mg/mL is 1,000,000 ng/mL. Six orders of magnitude separate these units, which is roughly the distance between the concentration a compound is stored at and the concentration it is measured at.

1 mg/mL is 1000 µg/mL. Only the mass prefix changes — the millilitre is the same millilitre on both sides — so this is the simplest kind of concentration conversion there is: multiply by a thousand.

They are the same. 1.8 µg/µL is 1.8 mg/mL. Scale the mass down by a thousand and the volume down by a thousand and the concentration does not move.

An ounce is 28,349.523125 milligrams. The two units sit four and a half orders of magnitude apart, which is the whole reason this conversion is awkward: anything measured in milligrams is a fraction of an ounce too small to say out loud.

Five hundred millilitres of water weighs 1.10 pounds. The same volume of honey weighs 1.58. This pairing — a metric volume against an imperial weight — usually means a bottle or a sample measured in one system and shipped, priced or posted in the other. That crossing is where the substance stops being obvious to the search engine and stays obvious to the person searching. They know what is in the bottle. The box just does not ask.

Most people who search "ml to mg" are holding a syringe or a bottle of liquid medicine, and for them the honest answer is that this conversion is not the one they need. A 5 mL spoonful of paracetamol suspension is not 5000 mg of paracetamol; it is 5 mL of a liquid that contains 120 mg of it. The number that turns volume into dose is printed on the label as a concentration. This page does the density conversion — mass and volume for a substance — and says plainly when that is the wrong tool.

1 ng/L is 0.000001 mg/L, and 1 mg/L is 1,000,000 ng/L. This conversion spans the gap between what a modern trace method can detect and the scale most drinking-water limits are written at.

1 ng/mL is 0.001 mg/L. The two units measure the same thing — a mass of something dissolved in a volume of liquid — so converting between them moves a decimal point and nothing else. Going the other way, 1 mg/L is 1000 ng/mL.

They are the same concentration. A result of 30 ng/mL is 30 µg/L. The factor is exactly 1, and laboratories in different countries report the same measurement in whichever of the two their convention prefers.

1000 ng/mL is 1 µg/mL. Only the mass prefix changes, so this is a plain division by a thousand — the concentration at which an assay reads and the concentration at which a reagent is supplied, one decade-cubed apart.

1000 ng/µL is 1 mg/mL. Both prefixes change here, which is why this pair is the one people check twice: the mass drops a million-fold and the volume a thousand-fold, and what survives is a single thousand.

1000 ng/µL is 1 µg/µL. The microlitre does not move, so this is a plain thousand between the unit a quantification instrument reports and the unit a concentrated preparation is described in.

1 pg/mL is 0.1 ng/dL, and 1 ng/dL is 10 pg/mL. The factor is ten — not the thousand most unit pairs here carry — because the decilitre is only a hundred times the millilitre while the nanogram is a thousand times the picogram.

They are the same. 5 pg/mL is 5 ng/L. The picogram is a thousandth of a nanogram and the millilitre a thousandth of a litre, so the two thousands cancel and the number survives the rename untouched.

Two units, one volume, and a factor of a thousand. pg/mL and ng/mL both measure a mass of solute in one millilitre of solution, so the only thing that changes between them is the prefix on the gram — and picograms are a thousand times smaller than nanograms.

A US gallon of water weighs 8.33 pounds. Of olive oil, 7.62. Of honey, 11.9. So "how many gallons is a pound" has no answer on its own — it has one answer per substance, and the spread between them is far larger than any rounding this page could do. The substance is a field here, not an assumption.

Sixteen ounces make a pound — exactly, by definition, with nothing rounded. The arithmetic is the easy part of this conversion; knowing which ounce someone means is the part that goes wrong.

µg/dL reads as micrograms per decilitre: how many millionths of a gram sit in one tenth of a litre of solution. It is the unit blood lead, cortisol and serum iron are usually reported in, which is why it turns up on a report next to figures written per litre and has to be reconciled with them.

1 µg/L is 1000 ng/L. This is the step down into trace analysis: once a contaminant is measured in parts per trillion rather than parts per billion, µg/L stops being a readable unit and ng/L takes over.

They are the same. 4 µg/mL is 4 mg/L, 0.7 µg/mL is 0.7 mg/L, and the factor between the units is exactly 1 — not approximately, not for dilute solutions only, but always and for every substance.

50 ng/µL is 50 µg/mL. The two units scale mass and volume by the same thousand, so the number survives the rename untouched — the factor is exactly 1.

1000 µg/mL is 1 µg/µL. This is the mirror image of the usual case — the mass unit does not move at all, and the thousand comes entirely from the volume.

Nine tenths of the mass-to-volume pairs anyone searches for are the same arithmetic with different unit labels. Quarts to pounds, cc to ounces, millilitres to kilograms, decilitres to ounces — each is one division by a density, and none of them has anything to say that the others do not. So they share a page. Pick the pair from the presets or set the two units yourself, choose a substance, and the answer comes with the density it used and where that density came from.