Scientific Calculator
Full-featured scientific calculator with trigonometry, logarithms, exponents, and more.
Quick Reference
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About This Calculator
Need a powerful scientific calculator online? Our free Scientific Calculator brings the full functionality of a TI-84 or Casio fx-991 right to your browser—no downloads, no apps, no cost. Whether you're solving trigonometry homework, calculating logarithms for chemistry, or working through calculus problems, this calculator handles everything from basic arithmetic to advanced mathematical functions with precision to 15 significant digits.
What makes this scientific calculator essential? It supports all standard functions including sin, cos, tan (and their inverses), natural and common logarithms (ln and log), exponentials, powers, roots, factorials, and permutations. Toggle between degree and radian modes for trigonometric calculations. Use memory functions to store intermediate values. Access hyperbolic functions (sinh, cosh, tanh) through the 2nd function key. The calculation history lets you review and reuse previous results instantly.
Over 2 million calculations are performed monthly on this calculator by students, engineers, scientists, and professionals who need reliable, instant results. Whether you're preparing for the SAT, working through physics homework, or solving real-world engineering problems, this scientific calculator delivers the precision and functionality you need—completely free and available 24/7.
How to Use the Scientific Calculator
- 1Enter numbers using the on-screen buttons or your keyboard (numpad supported).
- 2Select trigonometric functions (sin, cos, tan) or their inverses from the function panel.
- 3Toggle between DEG and RAD modes for angle measurements in trigonometric calculations.
- 4Use the 2nd button to access inverse functions (sin⁻¹, cos⁻¹, tan⁻¹) and hyperbolic functions.
- 5Apply logarithmic functions: ln for natural log (base e), log for common log (base 10).
- 6Use parentheses ( ) to control order of operations in complex expressions.
- 7Press = or Enter to calculate the result; use ANS to reference your previous answer.
- 8Leverage memory functions (MC, MR, M+, M-, MS) to store and recall values during multi-step calculations.
Complete Function Reference
This scientific calculator includes every function you'd find on a physical TI-84 or Casio fx:
Trigonometric Functions:
| Function | Description | Example (DEG mode) |
|---|---|---|
| sin | Sine | sin(30°) = 0.5 |
| cos | Cosine | cos(60°) = 0.5 |
| tan | Tangent | tan(45°) = 1 |
| sin⁻¹ | Inverse sine (arcsin) | sin⁻¹(0.5) = 30° |
| cos⁻¹ | Inverse cosine (arccos) | cos⁻¹(0.5) = 60° |
| tan⁻¹ | Inverse tangent (arctan) | tan⁻¹(1) = 45° |
Hyperbolic Functions (2nd mode):
| Function | Description | Relation |
|---|---|---|
| sinh | Hyperbolic sine | (eˣ - e⁻ˣ)/2 |
| cosh | Hyperbolic cosine | (eˣ + e⁻ˣ)/2 |
| tanh | Hyperbolic tangent | sinh(x)/cosh(x) |
| asinh | Inverse hyperbolic sine | ln(x + √(x² + 1)) |
| acosh | Inverse hyperbolic cosine | ln(x + √(x² - 1)) |
| atanh | Inverse hyperbolic tangent | ½ln((1+x)/(1-x)) |
Logarithmic & Exponential:
| Function | Description | Example |
|---|---|---|
| ln | Natural logarithm (base e) | ln(e) = 1, ln(10) ≈ 2.303 |
| log | Common logarithm (base 10) | log(100) = 2, log(1000) = 3 |
| eˣ | Exponential (e to the power x) | e² ≈ 7.389 |
| 10ˣ | Power of 10 | 10³ = 1000 |
Powers & Roots:
| Function | Description | Example |
|---|---|---|
| √ | Square root | √144 = 12 |
| ∛ | Cube root (2nd mode) | ∛27 = 3 |
| x² | Square | 7² = 49 |
| xʸ | Power (any exponent) | 2¹⁰ = 1024 |
| n! | Factorial | 5! = 120 |
Degree vs Radian Mode: When to Use Each
Understanding angle measurement is crucial for correct trigonometric calculations:
Degrees (DEG) - Use When:
- Working with angles in everyday applications
- Navigation and compass directions
- Construction and architecture measurements
- Most pre-calculus math problems
- Problems that mention "degrees" or use the ° symbol
Radians (RAD) - Use When:
- Calculus problems (derivatives, integrals of trig functions)
- Physics equations (angular velocity, wave functions)
- Engineering calculations
- Problems involving π directly
- When the problem uses "rad" or no unit
Conversion Formulas:
Radians = Degrees × (π/180)
Degrees = Radians × (180/π)
Essential Angle Values:
| Degrees | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 0.5 | 0.866 | 0.577 |
| 45° | π/4 | 0.707 | 0.707 | 1 |
| 60° | π/3 | 0.866 | 0.5 | 1.732 |
| 90° | π/2 | 1 | 0 | undefined |
| 180° | π | 0 | -1 | 0 |
| 270° | 3π/2 | -1 | 0 | undefined |
| 360° | 2π | 0 | 1 | 0 |
Common Mistake: Getting unexpected results because you're in the wrong mode. If sin(30) gives you -0.988 instead of 0.5, you're in radian mode!
Memory Functions for Complex Calculations
Master the memory functions to handle multi-step calculations efficiently:
| Button | Function | Description |
|---|---|---|
| MC | Memory Clear | Clears stored memory value to 0 |
| MR | Memory Recall | Displays current memory value |
| M+ | Memory Add | Adds display value to memory |
| M- | Memory Subtract | Subtracts display value from memory |
| MS | Memory Store | Stores current display value in memory |
Practical Example - Quadratic Formula: Solving x² + 5x + 6 = 0 using x = (-b ± √(b²-4ac)) / 2a
- Calculate discriminant: 5² - 4(1)(6) = 25 - 24 = 1
- Press MS to store the discriminant (1)
- Calculate √(MR) = √1 = 1
- Calculate (-5 + 1) / 2 = -2 ← First root
- Calculate (-5 - 1) / 2 = -3 ← Second root
Running Total Example: Calculating a shopping list total with tax:
- Enter 15.99, press MS (store)
- Enter 24.50, press M+ (memory = 40.49)
- Enter 8.75, press M+ (memory = 49.24)
- Press MR to see subtotal (49.24)
- Calculate MR × 1.08 for 8% tax = 53.18
A small "M" indicator appears when a value is stored in memory.
Order of Operations (PEMDAS/BODMAS)
This calculator follows standard mathematical order of operations:
The Hierarchy:
- Parentheses / Brackets - Evaluate innermost first
- Exponents / Orders - Powers, roots, factorials
- Multiplication & Division - Left to right
- Addition & Subtraction - Left to right
Examples:
2 + 3 × 4 = 2 + 12 = 14 (not 20)
(2 + 3) × 4 = 5 × 4 = 20
8 ÷ 2(2 + 2) = 8 ÷ 2 × 4 = 16 (left to right after parentheses)
2³ + 4 × 5 = 8 + 20 = 28
Nested Parentheses: Work from innermost to outermost:
((3 + 2) × 4 - 10) ÷ 2
= (5 × 4 - 10) ÷ 2
= (20 - 10) ÷ 2
= 10 ÷ 2
= 5
Functions Take Priority: Function arguments are evaluated first:
sin(30 + 15) = sin(45°) ≈ 0.707
log(10 × 10) = log(100) = 2
ANS Function: Use ANS to chain calculations using your previous result:
- Calculate 2 × 3 = 6
- Calculate ANS + 4 = 10 (uses 6 from previous result)
- Calculate ANS² = 100 (uses 10 from previous result)
Real-World Applications by Field
Engineering:
- Circuit analysis: V = IR, P = I²R
- Structural loads: Using sin/cos for force components
- Signal processing: Fourier transforms with complex exponentials
- Control systems: Transfer functions with logarithmic scales
Physics:
- Projectile motion: y = v₀sin(θ)t - ½gt²
- Wave equations: y = A sin(ωt + φ)
- Optics: n₁sin(θ₁) = n₂sin(θ₂) (Snell's law)
- Quantum mechanics: Wave functions with exponentials
Chemistry:
- pH calculations: pH = -log[H⁺]
- Rate equations: k = Ae^(-Ea/RT) (Arrhenius equation)
- Dilution: C₁V₁ = C₂V₂
- Half-life: N = N₀e^(-λt)
Finance & Economics:
- Compound interest: A = P(1 + r/n)^(nt)
- Present value: PV = FV × e^(-rt)
- Logarithmic returns: r = ln(P₁/P₀)
- Exponential growth models
Computer Science:
- Algorithm complexity: O(log n), O(n log n)
- Probability: Permutations and combinations
- Cryptography: Modular exponentiation
- Graphics: Rotation matrices using sin/cos
Solving Common Math Problems
Quadratic Equations (ax² + bx + c = 0): Use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Example: 2x² + 5x - 3 = 0
- Calculate b² - 4ac = 25 - 4(2)(-3) = 25 + 24 = 49
- √49 = 7
- x₁ = (-5 + 7) / 4 = 0.5
- x₂ = (-5 - 7) / 4 = -3
Exponential Equations: Solve 2ˣ = 32
- Take log of both sides: x × log(2) = log(32)
- x = log(32) / log(2) = 1.505 / 0.301 = 5
- Verify: 2⁵ = 32 ✓
Trigonometric Equations: Solve sin(x) = 0.5 (for 0° ≤ x ≤ 360°)
- Primary solution: sin⁻¹(0.5) = 30°
- Secondary solution: 180° - 30° = 150°
- Solutions: x = 30° or x = 150°
Logarithmic Equations: Solve log(x) + log(x-3) = 1
- Combine: log(x(x-3)) = 1
- Convert: x(x-3) = 10
- Expand: x² - 3x - 10 = 0
- Factor: (x-5)(x+2) = 0
- x = 5 (reject x = -2, can't take log of negative)
Scientific Notation and Large Numbers
The calculator automatically switches to scientific notation for very large or very small numbers:
Understanding Scientific Notation:
- 1.5e10 means 1.5 × 10¹⁰ = 15,000,000,000
- 3.2e-8 means 3.2 × 10⁻⁸ = 0.000000032
Common Values in Scientific Notation:
| Value | Scientific | Standard |
|---|---|---|
| Speed of light | 3e8 m/s | 300,000,000 m/s |
| Avogadro's number | 6.022e23 | 602,200,000,000,000,000,000,000 |
| Electron mass | 9.109e-31 kg | 0.0000000000000000000000000000009109 kg |
| Planck's constant | 6.626e-34 J·s | Very small! |
Entering Scientific Notation: Use the EE or EXP button (or type 'e'):
- To enter 5.5 × 10⁶: Type 5.5, press EE, type 6
- To enter 3 × 10⁻⁴: Type 3, press EE, type -4
Precision Limits: This calculator maintains 15-16 significant digits (JavaScript's IEEE 754 double precision). Results beyond this precision may show rounding errors:
- Valid: 123456789012345 (15 digits)
- May show errors: 12345678901234567890 (too many digits)
Constants and Special Values
Built-in Constants:
| Constant | Value | Usage |
|---|---|---|
| π (pi) | 3.14159265359... | Circle calculations, trig in radians |
| e (Euler's) | 2.71828182846... | Natural logarithms, compound interest |
Important Mathematical Values:
| Expression | Value | Context |
|---|---|---|
| √2 | 1.41421356... | Diagonal of unit square |
| √3 | 1.73205080... | Equilateral triangle heights |
| ln(2) | 0.69314718... | Doubling time calculations |
| log(2) | 0.30102999... | Binary/decimal conversions |
| 1/π | 0.31830988... | Inverse circle calculations |
| e^π | 23.1406926... | Gelfond's constant |
Special Results:
| Operation | Result | Reason |
|---|---|---|
| 0! | 1 | By definition (empty product) |
| 1/0 | Infinity | Division by zero |
| 0/0 | NaN | Undefined |
| √(-1) | Error | Not real (use complex calc) |
| ln(0) | -Infinity | Limit as x→0⁺ |
| tan(90°) | Infinity | Undefined at 90° |
Physical Constants Reference:
| Constant | Symbol | Value |
|---|---|---|
| Speed of light | c | 299,792,458 m/s |
| Planck's constant | h | 6.626 × 10⁻³⁴ J·s |
| Avogadro's number | Nₐ | 6.022 × 10²³ /mol |
| Boltzmann constant | k | 1.381 × 10⁻²³ J/K |
| Electron charge | e | 1.602 × 10⁻¹⁹ C |
| Gravitational constant | G | 6.674 × 10⁻¹¹ N·m²/kg² |
| Earth gravity | g | 9.80665 m/s² |
| Proton mass | mₚ | 1.673 × 10⁻²⁷ kg |
| Standard atmosphere | atm | 101,325 Pa |
| Molar gas constant | R | 8.314 J/(mol·K) |
| Faraday constant | F | 96,485 C/mol |
Pro Tips
- 💡Use the ANS button to reference your previous result—essential for chained calculations and iterative problems.
- 💡Store intermediate values with MS (Memory Store) and recall them with MR—perfect for complex formulas with repeated terms.
- 💡Parentheses are your friend: when in doubt, use them to ensure correct order of operations.
- 💡Switch to RAD mode for calculus problems; most derivatives and integrals assume radians.
- 💡The history section lets you click any previous result to use it immediately—great for trial-and-error problem solving.
- 💡For percentage calculations in scientific context: 50% = 0.5, so divide percentages by 100 before using.
- 💡Use log for decibels (dB = 10 log(P₁/P₂)) and pH calculations (pH = -log[H⁺]).
- 💡Learn keyboard shortcuts for speed: the numpad plus *, /, +, -, Enter makes you faster than clicking.
- 💡Verify trigonometry answers by checking: sin²(x) + cos²(x) should always equal 1.
- 💡For very small or large numbers, the calculator automatically uses scientific notation (e.g., 1.5e10).
- 💡When solving equations, use the memory to store coefficients and avoid retyping values.
- 💡Compare to known values: sin(30°) = 0.5, cos(60°) = 0.5, tan(45°) = 1—use these to verify DEG/RAD mode.
Frequently Asked Questions
Click the DEG or RAD button at the top of the calculator. DEG mode (default) interprets angles in degrees (360° in a circle). RAD mode interprets angles in radians (2π in a circle). Most everyday problems use degrees, while calculus and physics typically use radians. If you get unexpected trigonometry results, check this setting first.
