Formulas and sources
Each formula this calculator uses, where it comes from, and what it leaves out.
Order of operations
Brackets come first, with the number inside sin, cos, tan or √. Next come powers (^), right to left, so 2^3^2 is 2^9 = 512. A minus sign in front of a number applies after a power on its right, so -2^2 is -4 and (-2)^2 is 4; spreadsheets such as Excel read -2^2 as 4. A negative result or recalled number goes in brackets first, so it is raised as a whole. Multiplication and division follow, left to right, and a number next to a bracket is multiplied at this step, so 6÷2(1+2) is 9. Addition and subtraction come last, left to right. A bracket left open at = is closed for you.
Source: The conventional order, as the Common Core State Standards for Mathematics name it in 6.EE.A.2.c [1]; each pair left to right, as the Progressions explain it [2]. The leading minus follows written algebra; no standard states it. Implicit multiplication: CalcTrail’s own; no publisher.
Percent key (%)
On its own, or after × or ÷, B% is B ÷ 100, so 200 × 10% is 20 and 200 ÷ 10% is 2,000. After + or −, B% is B percent of everything to its left, so 200 + 10% is 220 and 200 + 10% + 5% is 231. The % key needs a plain number before it, so (5+5)% is refused.
Source: A percent as a rate per 100: Common Core State Standards for Mathematics, 6.RP.A.3.c [1]. The add-on reading after + or −: CalcTrail’s own rule; no publisher.
Sci row: sin, cos, tan, √, xʸ and π
- X
- the angle, in degrees
cos and tan work as sin does; angles are in degrees only. tan has no answer at 90°, 270° and every 180° from them, and √ needs a number of 0 or more. π is 3.141592653589793, and it cannot be stored exactly, so sin(180) shows 1.225e-16 rather than 0.
Source: The degree as NIST defines it, 1° = π/180 rad [3]. The functions and π as the NIST Digital Library of Mathematical Functions defines them [4] [5], computed as ECMA-262 allows [6].
Errors
A division by zero shows Error with a message that division by zero is not allowed. That covers 0 ÷ 0 and a divisor that works out to zero, such as (1 − 1). A square root of a negative number and tan(90°) have no real answer, and a result too large to hold is refused. An error never goes on the tape.
Source: Division by zero is undefined: standard rule; no single publisher. The messages are CalcTrail’s own.
Rounding and display
Each result is rounded to 15 significant digits, and that is what the tape keeps. The display adds no padding zeros: up to two decimals from 1 up, so 2 + 3 shows 5, and up to ten significant digits below 1, so 1 ÷ 3 shows 0.3333333333. From 10^15 up and from 10^-9 down, results show in exponential form with up to three decimals, so 10^16 shows 1e+16.
Source: CalcTrail’s own display rules; no publisher.
Memory keys
M+ works out the calculation in progress and adds its result to memory; M− subtracts it. MR puts the stored number into your entry: after an operator it is the next number, and after a number it is multiplied in. MC clears memory; AC does not.
Source: CalcTrail’s own; no publisher.
Tape total
With Show Overall Total ticked
The total is the sum of the results of the lines on screen, so a search gives a subtotal. It is rounded to 15 significant digits, as each line is: lines of 0.1 and 0.2 total 0.3.
Source: Standard formula; no single publisher.
Sources
- National Governors Association Center for Best Practices and Council of Chief State School Officers. Common Core State Standards for Mathematics, standards 6.EE.A.2.c (order of operations) and 6.RP.A.3.c (percent). 2010.
- Common Core Standards Writing Team. Progressions for the Common Core State Standards for Mathematics, Expressions and Equations, grades 6 to 8, p. 176. Institute for Mathematics and Education, University of Arizona, February 28, 2023.
- National Institute of Standards and Technology. NIST Guide to the SI, Chapter 5: Units Outside the SI, Table 6, the degree. Special Publication 811 (2008), web page updated December 8, 2025.
- National Institute of Standards and Technology. NIST Digital Library of Mathematical Functions, §4.14, sine, cosine and tangent, and §4.23, their inverses. Release 1.2.8, September 15, 2026.
- National Institute of Standards and Technology. NIST Digital Library of Mathematical Functions, §3.12, π (3.12.1) and e (3.12.3). Release 1.2.8, September 15, 2026.
- Ecma International, TC39. ECMAScript Language Specification (ECMA-262), §21.3.2, Function Properties of the Math Object, the note. Living standard, titled ECMAScript 2027, read October 4, 2026.
What this calculator does not cover
- Degrees only, with sin, cos, tan, √, xʸ and π. It has no e, log, factorial, constants or angle setting; the Scientific Calculator has them.
- Real numbers, one expression at a time, to 15 significant digits. The keypad cannot put a minus straight after ×, ÷ or xʸ; use ± or a bracket.
- The tape keeps the last 100 lines.
Sources checked on .