Scientific Calculator

How the scientific calculator reads your expression

Everything you type is evaluated as one expression rather than as a running total, so the ordinary rules of precedence apply exactly as they would on paper. Brackets are resolved first, then powers, then multiplication and division, and finally addition and subtraction. That means 2 + 3 × 4 is 14, not 20, and (2 + 3) × 4 is 20.

Two details are worth knowing because they are where calculators most often disagree with each other. Powers are right-associative, so 2^3^2 is 2⁹ = 512 rather than 8² = 64. And a leading minus sign is applied after the power, so -2^2 is −4; bracket the negative number if you want −2 squared.

What each group of keys does

The left-hand block holds the functions: sine, cosine and tangent with their inverses above them, the constants π and e, natural log (ln) and base-10 log (log), square root, cube root, and the power keys. The middle block is the numeric keypad with the decimal point and EXP for scientific notation: 2 EXP 5 is 2 × 10⁵. The right-hand column carries the arithmetic operators, Back to delete one character, AC to clear everything, and the memory keys.

The factorial key n! multiplies every whole number from 1 up to the value in front of it, so 5! is 120. It only accepts whole numbers of zero or more, and stops at 170 because 171! is larger than this number format can hold. In each of those cases the calculator says so rather than showing a misleading answer.

Scientific calculator vs four function calculator

A four function calculator, sometimes written 4 function calculator, handles addition, subtraction, multiplication and division, plus square root and percent on a good model. A basic four function calculator is enough for shopping, budgeting and most arithmetic in the early grades, which is why it often appears on school supply lists for younger students. A scientific calculator adds the functions that algebra, geometry, chemistry and physics lean on: trigonometry, logarithms, powers, factorials and memory. This page is a non graphing calculator. It evaluates a numerical expression and shows one answer rather than plotting a curve, which keeps it fast and means it needs no account or setup.

Inverse functions: sin⁻¹, cos⁻¹ and tan⁻¹

Each trigonometric key has an inverse above it, and the inverse answers the opposite question: given the ratio, what is the angle? Searches for a tan inverse calculator, an inverse cosine calculator or a calculator with inverse functions all mean these keys. To use inverse trig on calculator hardware you normally press a shift or 2nd key first; here the inverse sits directly above its partner. In degree mode the result is an angle in degrees. A quick check is the sine inverse of 1/2: it is 30°, because sin 30° = 0.5, so a search for sin 1/2 and a search for its inverse describe the same fact read in opposite directions. The table lists the results worth knowing by heart.

Scientific notation and standard form on a scientific calculator

The EXP key enters a power of ten, so 6.02 EXP 23 is 6.02 × 10²³, Avogadro's number. Anyone looking for a scientific notation calculator, a standard form calculator (the British name) or an exponential notation calculator needs this key. On a standard form on calculator display you will often see 6.02E23, where the E means times ten to the power. For scientific notation computation such as (3 × 10⁸) × (2 × 10⁻⁵), type 3 EXP 8 × 2 EXP −5 and read 6000, which is 6 × 10³. If you only need to convert between decimal and scientific form, the scientific notation calculator on this site does that and shows the significant figures. The same task goes by sci not calculator, scientific notation calc and standard notation calculator when the goal is the plain decimal.

Powers, roots and negative exponents

Powers use the ^ key. A negative exponent means a reciprocal, so 2^−3 is 1/8 = 0.125. People who search for exponents to negative power often expect a negative answer, but the sign of the exponent moves the base to the other side of the fraction, not the sign of the result. Roots run the other way: what is the square root of 2? It is 1.414213562, an irrational number that never ends or repeats, so every calculator shows a rounded value. The cube root key handles roots such as the cube root of 27, which is 3, and any other root is a fractional power, since the nth root of x is x^1/n.

Logarithms and the ln x graph

Two log keys cover most needs: log is base 10 and ln is base e. ln(1) is 0, ln(e) is 1 and ln(10) is about 2.302585. The ln x graph crosses the x-axis at 1, climbs ever more slowly, and does not exist for zero or negative x, which is why the calculator reports an error for ln(0) or ln(−5) instead of a number. For a log in any other base, use the change of base rule log _b x = (ln x)/(ln b), or the log calculator on this site, which solves for an unknown base or argument as well.

Formulas worth running on a scientific calculator

A scientific calculator earns its keep on formulas. In physics, kinetic energy is E_k = 1/2 m v^2, so a 2 kg mass moving at 3 m/s carries 9 J. In chemistry, pH = -log _(10)[H^+] turns a hydrogen ion concentration of 0.001 into −log(0.001) = 3. In electronics, Ohm's law V = IR gives 6 V for 0.5 A through 12 Ω. Whether you call it a physics calculator or an engineering calculator, the trick is typing the whole formula as one expression with brackets, so the order of operations does the work. Other scientific formulas that suit the same approach include the quadratic formula, the sine rule and compound interest, as long as the numerator and denominator are bracketed.

What happens when you press equals

When you press equals, the whole line is read and evaluated with the precedence rules above rather than being computed key by key. That is why the expression stays visible, and why the tool works as a numerical expression calculator for anything you could write on one line. To perform the indicated operation in a textbook exercise, type the expression exactly as printed, using brackets where the page uses a fraction bar or a grouping symbol: (3 + 5) ÷ (7 − 3) is 2. Everything runs in your browser, so nothing you type is sent anywhere.

Accuracy and rounding

Results are computed in double-precision floating point and then rounded to twelve significant figures for display. That rounding is what turns the notorious 0.1 + 0.2 = 0.30000000000000004 into a plain 0.3. Twelve figures sits comfortably inside the roughly fifteen the format actually carries, so the rounding removes representation noise without inventing precision that is not there.

The same reasoning applies to trigonometry. Because π is irrational and cannot be stored exactly, sin(180°) computes to about 1.2 × 10⁻¹⁶ instead of zero; anything that small is reported as zero. Tangent is genuinely undefined at 90° and every 180° after it, so the calculator says so rather than returning the enormous number that floating point would otherwise produce.

Where it fits alongside the other math tools

This calculator is for one expression at a time. When the job is narrower, a dedicated tool shows more working. The exponent calculator handles powers and roots step by step, the statistics calculator takes a whole list of numbers for the mean, median and standard deviation, and the percentage calculator avoids the ambiguity of a % key altogether. For engineering coursework, statistics problem sets or a lab calculation that needs checking before it goes into a report, use this page for the arithmetic and the specialised tool for the working.