ΣCALCULATORWizard

🔬 Scientific Calculator

Full trig, logs, memory, 2nd shift functions, DEG/RAD mode, and keyboard support — the calculator that works the way you think.

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How to Use This Scientific Calculator

This calculator combines the full function set of a physical scientific calculator with the convenience of a browser-based tool that works identically on desktop, tablet, and mobile. You can type expressions directly using your keyboard or tap the on-screen buttons — both methods work simultaneously. Expressions are evaluated left-to-right respecting standard mathematical order of operations: parentheses first, then exponents, then multiplication and division, then addition and subtraction.

The 2nd button (top right of the mode bar) activates a second layer of functions. When 2nd is active, the function buttons shift: sin becomes sin⁻¹ (arcsine), cos becomes cos⁻¹ (arccosine), tan becomes tan⁻¹ (arctangent), log becomes 10ˣ (ten to the x), ln becomes eˣ (e to the x), √ becomes ∛ (cube root), x² becomes x³, and xʸ becomes ʸ√x (nth root). After pressing a shifted function, 2nd automatically deactivates. The yellow highlight on shifted buttons makes the active state obvious.

The DEG/RAD toggle controls how trigonometric functions interpret angles. DEG mode means sin(90) = 1 (90 degrees). RAD mode means sin(π/2) = 1 (pi/2 radians). The current mode is shown in the display badge and in the angle toggle. This setting also automatically affects inverse trig output — in DEG mode, asin(1) returns 90 (degrees); in RAD mode it returns π/2.

Complete Function Reference

sin / cos / tan
Trigonometric functions. Input angle in current mode (DEG or RAD). sin(30°) = 0.5
sin⁻¹ / cos⁻¹ / tan⁻¹
Inverse trig (2nd+sin/cos/tan). Returns angle. asin(0.5) = 30° in DEG mode
log
Base-10 logarithm. log(100) = 2. Used in pH, decibels, Richter scale
ln
Natural logarithm (base e). ln(e) = 1. ln(1) = 0. Used in growth/decay
10ˣ (2nd+log)
Ten to the x power. 10ˣ(3) = 1000. Inverse of log(x)
eˣ (2nd+ln)
e to the x power. eˣ(1) = 2.71828... Inverse of ln(x)
√ / ∛ (2nd)
Square root and cube root. √(16) = 4. ∛(27) = 3
x² / x³ (2nd)
Square and cube. Appends ^2 or ^3. 5x² = 25. 3x³ = 27
xʸ and ʸ√x
General power (x^y) and nth root (x^(1÷y)). 2^8 = 256. 8^(1÷3) = 2
π and e
Mathematical constants. π = 3.14159... e = 2.71828... Multiply naturally: 2π = 6.28318...
n!
Factorial. 5! = 120. 10! = 3,628,800. Works for integers 0–170
1/x
Reciprocal. 1/x wraps current expression. 1/4 = 0.25. 1/0.25 = 4
MC / MR / M+ / M−
Memory clear, recall, add to memory, subtract from memory. M badge shows when memory has a value
( and )
Group sub-expressions. Auto-closes open parens on =. (2+3)×4 = 20

Trigonometry: When to Use DEG vs RAD

Degrees and radians are two ways to measure angles. A full circle is 360° or 2π radians. The conversion is: radians = degrees × π/180. In everyday contexts — geometry, navigation, surveying, architecture — degrees are more intuitive. In calculus, physics, and higher mathematics, radians are preferred because the derivative of sin(x) is cos(x) only when x is in radians.

The unit circle provides the key reference values for trig functions. At 0° (0 rad): sin = 0, cos = 1, tan = 0. At 30° (π/6 rad): sin = 0.5, cos = √3/2 ≈ 0.866. At 45° (π/4 rad): sin = cos = √2/2 ≈ 0.707. At 60° (π/3 rad): sin = √3/2, cos = 0.5. At 90° (π/2 rad): sin = 1, cos = 0, tan = undefined (vertical). These values are worth memorizing for quick mental math.

Inverse trig functions return angles: asin(0.5) asks "what angle has a sine of 0.5?" The answer is 30° (in DEG mode) or π/6 ≈ 0.5236 (in RAD mode). Range restrictions apply: asin and acos return values in [-90°, 90°] and [0°, 180°] respectively; atan returns values in (-90°, 90°).

Logarithms: log vs ln and When to Use Each

The common logarithm (log, base 10) asks "what power of 10 gives this number?" log(1000) = 3 because 10³ = 1000. log(0.01) = -2 because 10⁻² = 0.01. It appears in the pH scale (pH = -log[H⁺], so a 10× increase in acidity drops pH by 1), decibels (dB = 10 log(P/P₀), the logarithmic sound measurement), and the Richter scale for earthquakes (each whole number increase represents 10× more ground motion amplitude).

The natural logarithm (ln, base e) uses Euler's number e = 2.71828... as its base. ln(e) = 1. It's the inverse of eˣ. Natural logs appear everywhere differential calculus is used: radioactive decay (N = N₀e⁻λt), compound interest (A = Pe^(rt)), population growth, and the normal distribution. The relationship between them is: ln(x) = log(x) / log(e) ≈ log(x) / 0.4343, or equivalently ln(x) = 2.303 × log(x).

Key logarithm rules every student should know: log(a×b) = log(a) + log(b). log(a/b) = log(a) − log(b). log(aʸ) = b × log(a). log(1) = 0. log(10) = 1 (base 10), ln(e) = 1 (base e). These rules allow you to break complex expressions into simpler parts — which is why logarithms were used as a computational shortcut before calculators existed.

Memory Functions Explained

The four memory buttons replicate the behavior of physical scientific calculators. M+ adds the currently displayed value to memory (e.g., after calculating a subtotal, press M+ to accumulate it). M− subtracts the current value from memory. MR recalls whatever is in memory and inserts it into the current expression — useful for referencing an intermediate result without retyping it. MC clears memory to zero.

Practical workflow: calculate the first sub-expression, press M+. Calculate the second sub-expression, press M+. Then press MR to use the accumulated total. The M badge in the display corner lights up whenever memory holds a non-zero value, preventing the common mistake of forgetting memory is active.

Keyboard Shortcuts

KeyActionKeyAction
0–9Append digitEnter / =Calculate
. (period)Decimal pointEscapeClear all (AC)
+ − * /OperatorsBackspaceDelete last character
( and )Parentheses%Percent operator
^ or **Power / exponentssin(
ccos(ttan(
llog(nln(
r√(pInsert π
eInsert e!Factorial

Frequently Asked Questions

Why does sin(90) = 1 but sin(90) give a weird number sometimes?
Make sure you're in DEG mode (not RAD). In RAD mode, sin(90) computes sin of 90 radians, which is approximately 0.894. For sin(90°) = 1, toggle the mode bar to DEG. The angle mode is always visible in the display badge so you can see which mode is active at a glance.
How do I calculate log base 2 (log₂)?
Use the change-of-base formula: log₂(x) = log(x) / log(2) = ln(x) / ln(2). For example, log₂(8) = log(8) / log(2) = 0.9031 / 0.3010 = 3. Type: log(8) ÷ log(2) and press =. Result: 3. This works for any base: logₙ(x) = log(x) / log(n).
How do I compute e to a power (exponential function)?
Two methods: (1) Press 2nd then the ln button to get eˣ, type your exponent, then press ). For example, eˣ(2) = 7.389. (2) Use the e constant button to insert e, then press ^ and type your exponent: e^2 = 7.389. Both give identical results.
What's the difference between xʸ and x²?
x² is a shortcut that appends ^2 after your current expression — press it right after a number to square it: 5 then x² gives 5^2 = 25. xʸ appends ^ and waits for you to type the exponent: 5 then xʸ then 3 gives 5^3 = 125. For the 2nd shifted version: ʸ√x appends ^(1÷ and waits for the root degree: 8 then ʸ√x then 3) gives 8^(1÷3) = 2 (cube root of 8).
How does implicit multiplication work?
The calculator automatically inserts a multiplication operator when a number is followed by a constant or parenthesis. 2π is interpreted as 2×π = 6.283. 3(4+5) is interpreted as 3×(4+5) = 27. Constants followed by numbers also work: π2 = 2π. This matches standard mathematical notation and prevents having to explicitly press × in most cases.
What's the maximum factorial this calculator can compute?
Factorials up to 170! are supported. 170! ≈ 7.26 × 10³⁰6. Beyond 170!, JavaScript's floating-point numbers overflow to Infinity. The calculator checks for this and will show an error message if you try to compute 171! or higher. For smaller factorials: 10! = 3,628,800 and 20! = 2,432,902,008,176,640,000.
Does the calculator support chained calculations?
Yes. After pressing =, if you immediately press an operator (+, −, ×, ÷), the result becomes the first operand of the next calculation. If you press a digit after =, the display clears and you start a new expression. If you press a function after =, the result is wrapped in that function: if the result is 4 and you press √, you get √(4) = 2.
How do I type negative numbers?
Two methods: (1) Press the ± button after typing a number to toggle its sign. (2) Type the minus/subtract key before the number — the expression handles leading minus. For negative numbers inside expressions: use parentheses for clarity, e.g., 5×(−3) to multiply 5 by negative 3.