A catalogue of different mathematical objects
The cards on this page do not offer interchangeable ways to get a number. They organise questions by the mathematical object that is known and the one that must be found. A planned drive starts with a distance, a consumption rate, and a pump price: 450 km ÷ 100 × 7.2 L × $1.85/L = $59.94. A fuel-economy result reverses the observation: litres used ÷ kilometres travelled × 100. One prices a future journey; the other describes a completed one. Keeping the direction of the calculation visible prevents a familiar unit from being used for the wrong question.
Scaling and comparing also use ratios, but their reference quantities differ. A six-portion batch from a four-portion recipe uses a scale factor of 6/4, turning 200 g of flour into 300 g. A test score of 18 out of 24 is 18/24 × 100 = 75%. Flour is multiplied because the yield changed; correct answers are divided by the available marks because the whole has not changed. The relevant calculator is the one whose denominator matches the real reference: original yield, total questions, distance, area, or time.
Examples identify the assumption behind each result
Some catalogue results are definitions, not measurements of every feature of a person or object. Body mass index uses kilograms divided by metres squared. At 70 kg and 1.75 m, the arithmetic is 70 ÷ 1.75² = 22.86. That screening number does not measure body composition, pregnancy, training status, or a diagnosis. A due-date calculation has a different kind of assumption: it counts calendar time from the date entered under a stated convention. It cannot replace clinical dating when the underlying date is uncertain.
Construction estimates start with shapes, then stop where the shape stops. A 12 ft by 10 ft rectangle contains 120 square feet. That is a sound material-area starting point, but it has not counted cut pieces, an alcove, a diagonal wall, damaged tiles, or a layout pattern. Conversions have a similarly sharp boundary. Ten kilograms equals about 22.05 pounds because both are mass; ten litres cannot become kilograms until a material density is supplied. A number with the wrong physical basis is not improved by more decimal places.
Time rules and energy boundaries change the equation
Date tools require a calendar rule before they can count. A business-day interval may omit Saturdays and Sundays while still including a public holiday unless that holiday has been entered separately. A time-zone offset is a difference between two stated offsets; it is not evidence that a region uses the same offset after a clock change. Preserve the start date, end date, location rule, and inclusion convention with a result so another person can reproduce the same count.
Energy estimates require a system boundary. Suppose a car needs 54 kWh at the battery and charging is 90% efficient. The wall energy is 54 ÷ 0.90 = 60 kWh; at $0.22 per kWh, the electricity cost is $13.20. Treating the stored 54 kWh as purchased energy would understate the bill. Conversely, using wall energy as though it were usable battery capacity would overstate the distance available. The two figures answer different operational questions.
Use a result as a documented scenario
These browser calculations are useful for checking arithmetic and comparing stated cases. They do not fetch an assessor's rule, a clinician's judgment, a retailer's final price, a local holiday list, a material density, or a current utility tariff. For a consequential decision, save the inputs, units, date, and source beside the result. That turns a temporary screen value into a scenario that can be checked, updated, or discussed with the person responsible for the real-world decision.