Calculation methodology
Review Calcr’s numerical precision, exact fractions, weighting rules, calendar conventions and the boundaries of each calculation.
Updated
Arithmetic and display precision
The scientific calculator evaluates permitted scalar real-number expressions with mathjs BigNumber arithmetic configured to 32 significant digits. Displayed results use up to 12 significant digits. Transcendental values and displayed decimals can be approximate. DEG is the initial angle mode; switch to RAD explicitly when needed. Postfix percent means division by 100, so 200 + 10% means 200.1.
Expressions have a length limit and an execution budget. Unsupported functions, non-real outputs, non-finite results and invalid operations are rejected. This calculator does not execute user programs or provide symbolic proofs.
Percentages, fractions and ratios
Percentages use the base appropriate to the chosen question. Change divides the difference by the original value and is undefined for an original value of zero.
Fraction arithmetic uses integer numerator/denominator operations, normalizes the sign and reduces by a greatest common divisor. Exact fractions remain distinct from decimal approximations. A zero denominator and division by a zero-valued fraction are invalid.
Ratio reduction scales nonnegative integer, decimal or fraction inputs to whole-number terms and divides by their greatest common divisor. Missing-term proportions use equivalent cross products and reject a division-by-zero case. Keep units and term order consistent.
Averages and grades
The arithmetic mean is sum / count, giving each number equal influence. The average calculator also shows the sorted middle value as the median, or the mean of the two middle values for an even count. The grade calculator uses percentage scores and positive percentage weights totaling 100. It does not treat a blank score as zero or silently rescale an incomplete set of weights. School-specific grading, extra credit and letter-grade conversions are outside its scope.
Calendar conventions
Date calculations use the Gregorian calendar and date-only values. A signed day difference is end minus start, independent of the user's time zone. Inclusive mode increases the range size by one while preserving direction; the same date counts as one inclusive day. The public date form adds or subtracts whole calendar days and includes weekends and holidays.
Age counts completed years, then completed months, then remaining days. Year and month candidates retain the original birth day where possible, clamping to the destination month's last day only when that day is invalid. Candidates are anchored to the original day rather than repeatedly advancing an already clamped date. Under this convention, a February 29 anniversary in a non-leap year is February 28. This is a calculation convention, not a rule for legal eligibility.
Clock durations and discounts
Clock duration subtracts minutes-after-midnight values, with 1,440 minutes added only when next day is explicitly selected. It excludes time-zone and daylight-saving transitions and does not deduct breaks.
Successive percentage discounts multiply the remaining-price factors. An optional entered sales-tax rate applies after the discounts. Amounts display two decimal places with half-up rounding. Shipping, fixed coupons and merchant-specific tax or rounding rules are not inferred. Keep full intermediate precision and compare the displayed price with the actual checkout.
Verification and corrections
Worked examples are intended to be reproducible with the listed inputs and modes. Important results should be independently checked. A result can be arithmetically correct yet inappropriate when the task uses a different convention. Report a discrepancy with a non-sensitive example using the contact instructions.
References: mathjs BigNumber documentation, OpenStax prealgebra and U.S. Naval Observatory leap-year rules. Product-specific conventions are stated above.