Scientific Calculator

How to use the scientific calculator

Type an expression with your keyboard — for example 2sin(30)+3^2 — or build it with the keys, then press = or Enter. The answer previews as you type, and the Working panel shows how the calculator read your input (with every hidden multiplication written out) and each step in the order it was done. Function keys open a bracket for you, and brackets you leave open at the end are closed automatically, so sin(30 works.

2nd swaps several keys to their inverse: sin⁻¹, cos⁻¹, tan⁻¹, eˣ, 10ˣ, ∛, x³, the y-th root and 1/x. Ans reuses the previous answer at full precision, and after = you can simply press an operator to carry on from it. Past calculations stay in the History list on this device, marked DEG or RAD so you know which unit was used.

Functions and how to type them

A few more work when typed: sinh, cosh, tanh and their inverses (asinh …), log2, exp, floor, ceil and round (halves round away from zero). Factorials work for whole numbers from 0! = 1 up to 170!, the largest that fits.

Order of operations

The calculator follows the conventional order: brackets and functions first, then powers, then multiplication and division from left to right, then addition and subtraction from left to right. A few cases trip people up:

• Powers stack from the top down. 2^3^2 is 2⁹ = 512, not 8² = 64.
• The minus sign comes after the power. −2^2 is −(2²) = −4; write (−2)^2 for 4. A power can be negative, though: 2^−2 = 0.25.
• A missing × is still ×. 2π = 6.28318530718 and 3(4+5) = 27. It has the same rank as ordinary × and ÷, so 1/2π is (1 ÷ 2) × π = 1.57079632679. To divide by 2π, write 1/(2π) = 0.159154943092.
• A function without brackets takes the next number. sin 30 + 1 is sin(30) + 1 = 1.5, and ln 5^2 is ln(25). When in doubt, add brackets; the “Read as” line shows what was understood.

Degrees vs radians

A full turn is 360 degrees or 2π radians, so radians = degrees × π ÷ 180 and degrees = radians × 180 ÷ π. The radian is the SI unit of angle — the angle at which the arc equals the radius — while the degree is accepted for everyday use. The same key press gives very different answers in the two modes: sin(30) is 0.5 in degrees but −0.988031624093 in radians, because 30 radians is about 1,718.87°. Use DEG for triangles, slopes, construction and navigation; use RAD for calculus, physics formulas with angular speed, and anything copied from code (JavaScript’s Math.sin expects radians). To convert a single angle, see degrees to radians or radians to degrees.

Worked example: how high does a ladder reach?

A 12 ft ladder leans against a wall, making a 75° angle with the ground. The height it reaches is the side opposite the angle, so height = 12 × sin(75°). In DEG mode type 12sin(75):

1. sin(75°) = 0.965925826289
2. 12 × 0.965925826289 = 11.5911099155 ft — about 11 ft 7 in (0.5911 ft × 12 ≈ 7.09 in).

To go the other way, press 2nd, sin, then type Ans ÷ 12 and =: sin⁻¹(11.5911099155 ÷ 12) gives back 75°. In radian mode the first step would silently use 75 radians, which is why the mode matters.

Common pitfalls

• Wrong angle mode — the most common reason a trig answer looks wrong. Check the DEG/RAD badge in the display.
• log vs ln — log(100) = 2, ln(100) ≈ 4.605. Formulas in chemistry (pH) and sound (decibels) use log; growth and decay use ln.
• EXP is not × 10 — 3E8 already means 3 × 10⁸. Also, 2e3 is 2,000 (scientific notation); for 2 × e³ write 2e^3 = 40.1710738464.
• Points where a function has no value — tan(90°), the log of 0 or a negative number, sin⁻¹(2) and the square root of a negative number are reported as errors, not as huge numbers.
• Display precision — answers show 12 significant digits. Values that should be exactly 0 or 0.5, such as sin(180°) or sin(30°), are shown exactly rather than as 1.2 × 10⁻¹⁶ or 0.49999999999999994.

For everyday sums with a memory and a tape, the basic online calculator is quicker; for percentages, try the percentage calculator.