Scientific Calculator
Trigonometry, logarithms, powers, roots, and mathematical constants — all in your browser. No app, no sign-up, no data sent anywhere.
What this calculator covers
A standard four-function calculator handles addition, subtraction, multiplication, and division. A scientific calculator extends that to the functions used across high school and university mathematics, physics, engineering, and computer science — the operations that appear constantly in coursework and professional work but aren't on a phone's default keypad.
This one handles trigonometry, logarithms, exponential functions, roots, and the constants π and e. It respects order of operations and bracket grouping, and lets you switch between degree and radian mode for trigonometric calculations.
Students
Working through trigonometry, pre-calculus, physics, or chemistry problems and need a reliable tool that handles the same functions as a TI-84 without carrying one around.
Engineers & architects
Quick trig checks for angles, gradients, load calculations, or signal processing. Useful during design review when you need a fast sanity check without opening specialised software.
Programmers
Checking logarithmic complexity, verifying bit-shift math, or working out floating-point edge cases without switching to a REPL or opening a spreadsheet.
Function reference
What each button does, when you'd use it, and a concrete example.
sincostanarcsinarccosarctanTrigonometry
Trigonometric functions relate angles to ratios of side lengths in a right triangle. Sine gives the ratio of the opposite side to the hypotenuse; cosine gives adjacent to hypotenuse; tangent gives opposite to adjacent. The arc- (inverse) functions reverse this: given a ratio, they return the angle.
Common uses
- › Calculating roof pitch or ramp angle from a gradient
- › Resolving force vectors in physics problems
- › Generating circular motion in graphics or simulations
- › Signal analysis (sine waves, Fourier components)
Example
A ladder 5m long leans against a wall at 60°. How high does it reach?
sin(60°) × 5 = 4.33m
Make sure the calculator is in degree mode for this.
loglnLogarithms
A logarithm asks: "what exponent do I need to reach this number?" log is base-10 (log₁₀), used in pH, decibels, and Richter scale. ln is the natural logarithm (base e ≈ 2.718), used in calculus, exponential growth/decay, and most physics and economics formulas.
Common uses
- › pH calculations (log₁₀ of hydrogen ion concentration)
- › Decibel levels in acoustics and electronics
- › Compound interest and population growth (ln)
- › Algorithmic complexity — O(log n) runtimes
Example
How many times must you halve 1,000,000 to reach 1?
log₂(1000000) = ln(1000000) / ln(2) ≈ 19.9
About 20 halvings — useful for binary search analysis.
x²x^y√xⁿ√xPowers and roots
Powers raise a number to an exponent (5³ = 125). Roots find the inverse — what number, multiplied by itself n times, gives this result? Square roots are the most common, but cube roots and higher-order roots appear regularly in volume calculations, signal processing, and statistics (standard deviation involves a square root).
Quick examples
2¹⁰ = 1024 (memory sizes in computing)
√144 = 12 (side of a 144m² square room)
4^0.5 = 2 (fractional exponents are roots)
³√27 = 3 (side length of a 27cm³ cube)
πeMathematical constants
π (pi) ≈ 3.14159265358979…
The ratio of a circle's circumference to its diameter. Appears in any formula involving circles, spheres, cylinders, or periodic functions. Used constantly in geometry, physics, and signal processing.
e (Euler's number) ≈ 2.71828182845904…
The base of the natural logarithm. Appears in exponential growth and decay, compound interest (continuous compounding), probability distributions, and differential equations.
Common mistakes and how to avoid them
Wrong angle mode (degrees vs. radians)
This is the most frequent error when using trig functions. If your problem gives angles in degrees (most geometry, surveying, navigation) but the calculator is in radian mode, every sin/cos/tan result will be wrong. sin(30°) = 0.5 — but sin(30 radians) ≈ −0.988. Always check the mode indicator before running trig calculations.
Forgetting order of operations with brackets
A common slip: typing 1/2+3 when you mean 1/(2+3). The calculator follows PEMDAS/BODMAS, so 1/2+3 = 3.5, not 0.2. Use brackets explicitly to group the denominator: 1/(2+3). When in doubt, add brackets — they never hurt.
Floating-point rounding (0.1 + 0.2 ≠ 0.3 exactly)
Computers store numbers in binary. Some decimal fractions — like 0.1 and 0.2 — can't be represented exactly in binary, so arithmetic on them produces tiny rounding errors (0.30000000000000004). For everyday calculation this is harmless. For financial or iterative engineering work, round explicitly at each step rather than relying on raw floating-point output.
Applying log to a negative number or zero
Logarithms are only defined for positive inputs. log(0) and log(−5) are undefined in real number mathematics (they involve complex numbers). If you see an error on a logarithm calculation, check whether the input has become zero or negative as a result of a prior step.
Real-world worked examples
A projectile is launched at 45° with an initial velocity of 20 m/s. What is its horizontal velocity component?
cos(45°) × 20 = 14.14 m/s
Use degree mode. cos(45°) = √2/2 ≈ 0.707
What is the pH of a solution with a hydrogen ion concentration of 0.001 mol/L?
−log(0.001) = −(−3) = 3
pH = −log₁₀[H⁺]. A result of 3 indicates a strong acid.
How long does it take for an investment to double at 7% annual interest (continuous compounding)?
ln(2) / 0.07 ≈ 9.9 years
Rule of 70 gives ~10 years; ln(2)/r is the precise formula.
A sorted list has 1,048,576 entries. How many comparisons does binary search need in the worst case?
log₂(1048576) = ln(1048576) / ln(2) = 20
1,048,576 = 2²⁰. Binary search is O(log n).
Runs entirely in your browser
Every calculation happens locally using JavaScript in your browser — the same engine that runs code in Chrome, Firefox, and Safari. Nothing is sent to a server. There's no logging, no session tracking, and no backend processing your numbers. It works offline after the initial page load.
Common questions
What's the difference between log and ln?
log (written log₁₀) asks 'what power of 10 gives this number?' — log(1000) = 3 because 10³ = 1000. ln is the natural logarithm, base e (≈ 2.718), and asks the same question but for powers of e. ln is more common in calculus, physics, and economics. log₁₀ is more common in chemistry (pH), acoustics (decibels), and logarithmic scale notation.
When should I use degrees vs. radians?
Use degrees when your problem states an angle in degrees — which is most geometry, navigation, surveying, and architecture. Use radians when working with calculus (derivatives of trig functions are clean in radians), physics (angular velocity, wave equations), or when a formula explicitly uses radians. A full circle is 360° or 2π radians.
Why does 0.1 + 0.2 not equal exactly 0.3?
Because computers use binary (base-2) arithmetic, and some decimal fractions can't be stored exactly in binary — similar to how 1/3 has no finite decimal representation. The tiny rounding error (0.30000000000000004) is a consequence of IEEE 754 double-precision arithmetic, which all modern CPUs use. For everyday calculations it doesn't matter. For financial software or long iterative calculations, you'd round explicitly at each step.
Can I use this for complex numbers or calculus?
Not currently. This calculator handles real-number arithmetic — trig, logarithms, powers, roots, and constants. Complex number operations (imaginary parts, polar form) and symbolic calculus (derivatives, integrals) are not supported. For those, tools like Wolfram Alpha or a CAS (computer algebra system) are more appropriate.
How accurate are the results?
The calculator uses IEEE 754 double-precision floating-point, which gives 15–17 significant decimal digits of accuracy. The constants π and e are stored at full double-precision (not truncated). For most academic and engineering uses this is more than sufficient.