Table of Contents
- What is this calculator?
- Calculation Modes
- Basic Arithmetic & COMP Mode
- Trigonometry & Angle Conversion
- Integration, Differentiation & Summation
- Statistics & Regression
- Matrix Calculator
- Complex Numbers
- Equation Solver
- BASE-N (Binary, Hex, Octal)
- Vector Calculator
- Scientific Constants & Unit Conversions
- Keyboard Shortcuts
- Frequently Asked Questions
1. What is this calculator?
This is a free online scientific calculator that emulates the Casio fx-991ES PLUS — the world's most popular scientific calculator, used in schools and universities globally. It replicates the physical calculator's display, button layout, and calculation logic entirely within your web browser.
All computations run locally using the math.js library. No data is sent to a server. Works offline after first load and can be installed to your home screen as a Progressive Web App (PWA).
- Integration calculator — numerical definite integrals with custom limits
- Derivative calculator — numerical differentiation at a point
- Matrix calculator — up to 3×3 matrices with full operation set
- Statistics calculator — 7 regression types + normal distribution
- Complex number calculator — rectangular and polar form
- Equation solver — quadratic, cubic, and simultaneous
- Fraction calculator — exact fraction arithmetic with simplification
- Binary / hex calculator — full BASE-N arithmetic with bitwise ops
2. Calculation Modes
Press MODE to switch between modes. The current mode is shown in the status bar at the top of the display.
COMP
General arithmetic, algebra, trigonometry, logarithms, roots, fractions, percentages
STAT
Single-variable statistics and 7 regression types with data table input
BASE-N
Integer arithmetic in binary, octal, decimal, and hexadecimal with bitwise operations
MATRIX
Matrix operations up to 3×3: add, subtract, multiply, determinant, inverse, transpose
VECTOR
2D and 3D vector operations: dot product, cross product, absolute value
TABLE
Evaluate a function f(x) over a range with a fixed step size
EQN
Solve simultaneous linear equations (2–3 unknowns), quadratic, and cubic equations
CMPLX
Complex number arithmetic in rectangular (a+bi) or polar (r∠θ) form
VERIF
Verify that an equation or inequality is true or false
3. Basic Arithmetic & COMP Mode
COMP mode handles everyday calculations and advanced mathematical functions.
Fractions
Enter fractions using the a b/c button. Results can be toggled between fraction and decimal with S⇔D.
1/3 + 1/6 → 1/22 3/4 × 4 → 11Percentages
200 × 15% → 30500 + 20% → 600Powers & Roots
2^10 → 1024∛(27) → 3 (cube root via SHIFT+√)⁵√(32) → 2 (5th root via ˣ√ wizard)DMS (Degrees, Minutes, Seconds)
Press the °'" button repeatedly to cycle through degree (°), minute ('), and second (") separators. Press = then °'" to convert a decimal angle to DMS.
1°30' → 1.5 (degrees)45° then °'" after result → 45°0'0"Engineering Notation
Press ENG to shift the result to the next higher engineering exponent (multiple of 3). Press SHIFT+ENG to shift to the next lower exponent.
Multi-statement
Separate multiple expressions with : (colon). Each result is shown in sequence when you press =.
3+4 : 10-2 → 7 then 8Memory Operations
| Operation | Button | Description |
|---|---|---|
| Store | SHIFT+RCL then A–F | Store current value into a memory variable |
| Recall | RCL then A–F | Recall stored value into expression |
| Answer | Ans | Insert the last computed result |
| Independent | M+, M−, MR | Add/subtract to M register, recall M |
CALC (Variable Substitution)
Enter an expression with a variable (e.g. X²+2X), press CALC, enter a value for X, and press =.
SOLVE (Numerical Solver)
Set up an equation with X, press SHIFT+CALC (SOLVE), provide an initial guess, and the calculator finds X numerically.
4. Trigonometry & Angle Conversion
Angle mode (Deg/Rad/Grad) is shown in the status bar. Switch with SHIFT+MODE.
| Function | Example | Result (Deg) |
|---|---|---|
sin(30) | sine 30° | 0.5 |
cos(60) | cosine 60° | 0.5 |
tan(45) | tangent 45° | 1 |
sin⁻¹(0.5) | arcsine | 30 |
sinh(1) | hyperbolic sine | 1.1752 |
Pol(3,4) | rectangular → polar | r=5, θ=53.13° |
Rec(5,53.13) | polar → rectangular | x=3, y=4 |
5. Integration, Differentiation & Summation
These are powerful tools for COMP mode. Results are numerical approximations, not symbolic.
Definite Integration (∫)
Computes the definite integral of f(x) from a to b numerically.
∫(f(x), lower, upper)∫(x², 0, 3) → 9∫(sin(x), 0, π) → 2∫(e^x, 0, 1) → 1.71828…Differentiation (d/dx)
Computes the numerical derivative of f(x) at a specific point x=a.
d/dx(f(x), a)d/dx(x³, 2) → 12d/dx(sin(x), 0) → 1Summation (Σ)
Computes the sum of f(x) for integer x from start to end.
Σ(f(x), start, end)Σ(x², 1, 5) → 55Σ(1/x, 1, 10) → 2.9289…6. Statistics & Regression
Switch to STAT mode, then select the regression type. Enter X (and Y) data into the data table, then access computed values via the STAT menu.
Regression Types
| # | Type | Model |
|---|---|---|
| 1 | 1-VAR | Single variable statistics |
| 2 | LinReg | y = A + Bx (linear) |
| 3 | QuadReg | y = A + Bx + Cx² (quadratic) |
| 4 | LogReg | y = A + B·ln(x) (logarithmic) |
| 5 | ExpReg | y = A·e^(Bx) (exponential) |
| 6 | PwrReg | y = A·x^B (power) |
| 7 | InvReg | y = A + B/x (inverse) |
Statistical Values (1-VAR)
After entering data, recall: n (count), x̄ (mean), σx (population std dev), sx (sample std dev), Σx, Σx², min, max, median, Q1, Q3.
Normal Distribution
P(t) — cumulative from 0 to tQ(t) — cumulative from t to ∞R(t) — cumulative from −∞ to t7. Matrix Calculator
Switch to MATRIX mode. Define matrices A, B, C (up to 3×3), then perform operations.
| Operation | How to |
|---|---|
| Addition / Subtraction | MatA + MatB |
| Multiplication | MatA × MatB |
| Scalar multiply | 3 × MatA |
| Determinant | det(MatA) |
| Inverse | MatA⁻¹ |
| Transpose | Trn(MatA) |
det(MatA) → −28. Complex Numbers (CMPLX Mode)
Switch to CMPLX mode. Use i (via ALPHA+ENG) for the imaginary unit.
| Operation | Example | Result |
|---|---|---|
| Addition | (3+4i) + (1−2i) | 4+2i |
| Multiplication | (1+i)² | 2i |
| Magnitude | Abs(3+4i) | 5 |
| Argument | arg(1+i) | 45° |
| Conjugate | Conj(3+4i) | 3−4i |
| Polar input | 5∠53.13° | 3+4i |
| Rect→Polar | press SHIFT+= (►) | switches display format |
9. Equation Solver (EQN Mode)
Switch to EQN mode, then select equation type. Enter coefficients and press = to solve.
Simultaneous Linear Equations
Quadratic Equations
Cubic Equations
10. BASE-N Calculator (Binary, Hex, Octal)
Switch to BASE-N mode. Use the sub-mode buttons to select BIN, OCT, DEC, or HEX. Results are automatically converted to the selected base.
Number Base Conversion
| Decimal | Binary (BIN) | Octal (OCT) | Hex (HEX) |
|---|---|---|---|
| 10 | 1010 | 12 | A |
| 255 | 11111111 | 377 | FF |
| 1024 | 10000000000 | 2000 | 400 |
Bitwise Operations
| Operation | Button | Example (BIN) | Result |
|---|---|---|---|
| AND | and | 1100 and 1010 | 1000 |
| OR | or | 1100 or 1010 | 1110 |
| XOR | xor | 1100 xor 1010 | 0110 |
| XNOR | xnor | 1100 xnor 1010 | complement of XOR |
| NOT | not | not(1010) | bitwise complement |
In HEX mode, press ALPHA to enter letters A–F.
11. Vector Calculator
Switch to VECTOR mode. Define vectors A, B (2D or 3D) and compute operations.
| Operation | Syntax | Example |
|---|---|---|
| Dot product | VctA · VctB | [1,2,3]·[4,5,6] = 32 |
| Cross product | VctA × VctB | [1,0,0]×[0,1,0] = [0,0,1] |
| Absolute value | Abs(VctA) | Abs([3,4]) = 5 |
12. Scientific Constants & Unit Conversions
Access via the CONST button (SHIFT+7). Constants include:
- Speed of light (c = 2.998×10⁸ m/s)
- Planck constant (h = 6.626×10⁻³⁴ J·s)
- Gravitational constant (G = 6.674×10⁻¹¹ N·m²/kg²)
- Electron mass, proton mass, neutron mass
- Avogadro constant (Nₐ = 6.022×10²³)
- Boltzmann constant, Faraday constant, gas constant
- Stefan-Boltzmann constant, Bohr magneton, atomic mass unit, and more
Unit conversion via CONV (SHIFT+8): length, area, volume, mass, temperature, speed, pressure, energy, and power.
13. Keyboard Shortcuts
| Key | Action |
|---|---|
0–9 | Input digits |
+ - * / | Arithmetic operators |
^ | Power (xⁿ) |
. | Decimal point |
( ) | Parentheses |
% | Percent |
! | Factorial |
: | Multi-statement separator |
Enter | Compute (=) |
Backspace | Delete last character |
Escape | All Clear (AC) |
← → | Move cursor in expression |
↑ ↓ | Browse expression history |
14. Frequently Asked Questions
Is this free to use?
Yes, completely free. No account, no subscription, no download required.
Does it work offline?
Once loaded, all calculations run locally in your browser with no internet connection needed. Install to your home screen as a PWA for full offline access.
Can I use it as a derivative calculator?
Yes. In COMP mode use d/dx(f(x), a) to compute the numerical derivative of any function at a point. Example: d/dx(x^3, 2) returns 12.
Can I use it as an integration calculator?
Yes. Use ∫(f(x), a, b) to compute a definite integral. Example: ∫(x^2, 0, 3) returns 9.
How do I enter complex numbers?
Switch to CMPLX mode. Type expressions like 3+4i where i is entered via ALPHA+ENG. Polar form: 5∠53.13 using the ∠ button.
How do I convert between binary and decimal?
Switch to BASE-N mode. Select your input base (BIN/OCT/DEC/HEX), type the number, and press the target base button — the result shows instantly in that base.
Can I solve quadratic equations?
Yes. Switch to EQN mode, select "Quadratic" (degree 2), enter a, b, c for ax²+bx+c=0, and press = to get both roots.
How do I input DMS (degrees, minutes, seconds)?
Type the degrees, press °'", type minutes, press °'" again, type seconds, press °'" a third time. Example: 45°30'15" evaluates to approximately 45.504°.
Is this the same as the physical Casio fx-991ES PLUS?
Functionally very similar. It emulates all major functions. Some advanced features (like multi-character variable names or certain CALC/SOLVE behaviors) may differ slightly from the hardware.
Does it work on mobile?
Yes. The calculator is fully responsive. On small screens, it scales automatically to fit the viewport. You can also install it as a PWA from your mobile browser.
How do I compute a summation (Σ)?
In COMP mode, use Σ(f(x), start, end). Example: Σ(x^2, 1, 10) computes 1²+2²+…+10² = 385.
Can I compute prime factorisation?
Yes. Enter a positive integer and press FACT (via the FACT button). Example: 360 → 2³×3²×5.
What is the calculation history?
Click the HIST button to open the history panel. It shows all previous expressions and results for the current session. Click any entry to reload its expression.
How do I compute logarithms with a custom base?
Use log(base, value) syntax. Example: log(2, 8) → 3 (log base 2 of 8). For natural log use ln(; for log base 10 use log(.