Calculators fall into a handful of families. What separates them is how much maths is built in, how you type a sum, and whether an exam will let you use one.
Basic
Four functions, a percent key and usually a single memory: the kind that lives in a kitchen drawer or beside a till. By 1977 an LCD model sold for $20 to $25, and the design has barely needed to change since.
One thing surprises people. A basic calculator works out each step as you press the keys, without applying the order of operations. Type 1 + 2 × 3 = and you get 9, not 7.
Scientific
Adds trigonometry, logarithms, powers, roots and statistics, and applies the standard order of operations. This is the school and university workhorse. The category arrived in 1972 with the HP-35, which made the slide rule obsolete within a few years. Most modern scientific calculators show the sum as you would write it in a textbook, with real fractions and powers.
Graphing
Plots functions on a screen, solves equations and runs statistics on lists of data. The Casio fx-7000G was the first, in 1985. In the US, the Texas Instruments TI-84 Plus has been the standard classroom model since 2004, at around $100.
CAS: calculators that do algebra
A computer algebra system (CAS) works with symbols, not just numbers. Ask it to expand (x + 2)2 and it answers x2 + 4x + 4. The HP-28C was the first handheld to do this, in 1987. Models such as the TI-89 and TI-Nspire CX CAS are powerful enough that the SAT and ACT both ban them.
Financial
Built for loans, mortgages, investments and cash flows, with keys for the number of payments (n), interest rate (i), present value (PV), payment (PMT) and future value (FV). The Hewlett-Packard HP-12C, launched in 1981, is still made and is one of HP's best-selling products ever. The Texas Instruments BA II Plus is its main rival. For most people, a web calculator built for one job is now easier.
Programmable
Stores routines you write yourself and runs them on demand. The HP-65 made this portable in 1974, with programs stored on small magnetic cards. Most graphing calculators are programmable today.
Printing
A desk calculator with a paper roll, descended from the Burroughs adding machines of the 1880s. Each entry is printed as you go, so you can check a long column of figures afterwards. Still sold for bookkeeping, where a paper trail helps.
Algebraic or RPN?
There are two ways to type a sum. Almost every calculator uses algebraic entry: you type it as you would write it. Some Hewlett-Packard models, including the HP-12C, use Reverse Polish Notation (RPN), where you enter the numbers first and the operation after.
| To work out (3 + 4) × 5 | You press |
|---|---|
| Algebraic | ( 3 + 4 ) × 5 = |
| RPN | 3 ENTER 4 + 5 × |
RPN needs no brackets and no equals key, and shows every intermediate result. It first appeared on the Friden EC-130 desk calculator in 1964. People who learn it tend to keep using it for life.
Which calculators exams allow
| Exam | Rule |
|---|---|
| SAT (digital) | A Desmos graphing calculator is built into the test app. You may also bring most graphing or scientific calculators. CAS models are no longer allowed, including every TI-89 and TI-92 and the TI-Nspire CAS. No calculator in Reading and Writing. |
| ACT | Most graphing and scientific calculators are allowed. CAS models are banned, including every TI-89 and TI-92, the HP Prime and the Casio ClassPad. |
| CFA | Only two models: the Texas Instruments BA II Plus (including the Professional) and the HP-12C (including the Platinum). |
Rules change, so check the exam board's current policy before test day. The sources below link to each one.
Software
The app on your phone, the box that appears in search results, and this website. With no physical keys to fit on, a software calculator can be as specific as it likes. Nobody would manufacture a plastic calculator for Georgia payroll withholding, but there is clearly a use for one.
The trade-off is trust. A physical calculator cannot go stale. A web calculator can sit unchanged for a year with a tax rate that changed in May, and nothing on the page will look wrong. That is the failure this site is built to avoid: every figure carries the document it came from and the date it was checked.
Quick answers
What are the main types of calculator?
Basic, scientific, graphing, CAS (computer algebra), financial, programmable, printing, and software calculators such as phone apps and websites.
What is the difference between a scientific and a graphing calculator?
A scientific calculator adds functions like trigonometry, logarithms and powers. A graphing calculator does all of that and can also plot functions on a screen, solve equations and handle lists of data.
What is a CAS calculator?
One with a computer algebra system, which works with symbols as well as numbers, for example expanding or factorising expressions. Both the SAT and the ACT ban them.
What calculator is allowed on the CFA exam?
Only the Texas Instruments BA II Plus (including the Professional) and the HP-12C (including the Platinum).
What is RPN on a calculator?
Reverse Polish Notation: you enter the numbers first and the operation after, so (3 + 4) × 5 is typed 3 ENTER 4 + 5 ×. It needs no brackets.
Sources
- Wikipedia, “Calculator”; Wikipedia, “Graphing calculator”
- Wikipedia, “Calculator input methods”; Smithsonian NMAH, Friden EC-130
- Wikipedia, “HP-28C”; Wikipedia, “HP-65”
- HP history, “A best seller” (HP-12C)
- ProMarket, Stigler Center, University of Chicago, on the TI-84 Plus
- College Board, SAT calculator policy
- ACT calculator policy
- CFA Institute calculator policy