Scientific Calculator
A free scientific calculator with trigonometry in degrees or radians, powers, roots, logarithms, factorials and percentages, plus memory, previous-answer recall and history.
How to use this calculator
Tap the keys or type straight into the display, then press = (or Enter). After a result, typing a number starts a new calculation, while pressing an operator such as + or × carries on from the answer. Ans inserts the previous answer, and Esc or AC clears everything.
- Functions such as sin, √x and log open a bracket for you: finish the value and close it with ).
- x², x³ and xʸ raise the number before them to a power; ʸ√x turns the number before it into a root, so 27 then ʸ√x then 3 ) gives the cube root of 27.
- EXP enters powers of ten: 1.5 EXP 3 means 1.5 × 10³.
- M+ and M− add the current value to memory or take it away; MR puts the memory into your expression and MC clears it.
- History keeps your recent calculations for this visit; tap one to use it again.
Order of operations
Calculations follow the usual order: brackets first, then factorials and percentages, then powers, then multiplication and division, and finally addition and subtraction. Powers are worked from right to left, and a minus sign in front of a power applies after the power.
2 + 3 × 4 = 14 2^3^2 = 2^9 = 512 −2^2 = −(2^2) = −4 (−2)^2 = 4
You can leave out the × in front of a bracket, a constant or a function: 2(3 + 4) means 2 × (3 + 4), and it is treated exactly like ×, so 1/2π means (1/2) × π.
Degrees or radians?
Choose Deg when angles are in degrees (a right angle is 90) and Rad when they are in radians (a right angle is π/2). The same key gives very different answers: sin(30) is 0.5 in degrees but about −0.988 in radians. In degree mode, common angles such as 30°, 45° and 90° give exact values, so sin(180) shows 0 rather than a tiny rounding error, and tan(90) is reported as undefined.
How precise are the answers?
Every calculation is carried out with 34 significant digits using decimal arithmetic, so 0.1 + 0.2 gives exactly 0.3. The display shows 12 significant digits, switching to powers of ten for very large or very small numbers, such as 170! = 7.25741561531 × 10^306.
Questions
Why does the calculator say a result has no real answer?
Some operations have no real-number result, for example the square root or logarithm of a negative number, or raising a negative number to a fractional power. For odd roots of negative numbers, use ∛x or ʸ√x: the cube root of −27 is −3.
How does the % key work?
x% always means x ÷ 100. So 50 + 10% is 50.1, and 200 × 15% is 30. For percentage problems such as increases or discounts, the percentage calculator has dedicated tools.
What is the largest factorial it can calculate?
170! is the largest, because 171! is bigger than the largest number the calculator can hold. Factorials of non-whole numbers, such as 0.5!, use the gamma function.
Sources
- OpenStax Prealgebra 2e, 2.1 Use the Language of Algebra (order of operations)
- OpenStax College Algebra 2e, 1.2 Exponents and Scientific Notation
- OpenStax Precalculus 2e, 5.1 Angles
- OpenStax Precalculus 2e, 5.2 Unit Circle: Sine and Cosine Functions
- OpenStax Precalculus 2e, 6.3 Inverse Trigonometric Functions
- NIST DLMF §4.2 Logarithm, Exponential, Powers: Definitions
- NIST DLMF §4.14 Trigonometric Functions: Definitions and Periodicity
- NIST DLMF §4.23 Inverse Trigonometric Functions
- NIST DLMF §5.2 Gamma Function: Definitions
- NIST DLMF §5.4 Gamma Function: Special Values and Extrema
- NIST DLMF §3.1 Arithmetics and Error Measures
Limitations
- Real numbers only: no complex results, so square roots of negatives, even roots of negatives, logs of non-positive numbers and negative bases with non-integer exponents are errors.
- Rational exponents are evaluated from their decimal value, so (-8)^(1/3) is a domain error even though a real cube root exists; use cbrt(-8) or root(-8, 3).
- Radian-mode snapping only recognizes arguments within 1e-30 relative of a multiple of π/2; values typed to many digits that are genuinely that close will display 0.
- No hyperbolic, statistical, base-conversion, fraction or complex-number functions (not offered by either audited keypad).
- Implicit multiplication has the same precedence as ×, so 1/2π means (1/2)·π, not 1/(2π); the normalized expression shows the explicit ×.
- Results beyond about ±1.8 × 10^308 are reported as overflow; the largest supported factorial is 170!.