Whether you are checking a trigonometry homework problem, converting a half-angle identity, or sanity-checking an exponent from a physics formula, a scientific calculator puts every transcendental function in one place. This free online scientific calculator evaluates the functions you actually reach for in math, science and engineering: sine, cosine and tangent, the square root, powers, natural and common logarithms, the exponential function e to the x, and factorial. Enter one number, pick your angle mode, and the result card returns the full set of values at once.
The engine uses the same correctly rounded IEEE 754 math-library routines that CPython's math module calls under the hood, so the digits you see agree with a physical handheld calculator and with Python itself.
How to Use
- Type the Value (x) you want to evaluate. Enter it as a decimal or a whole number; the field accepts any number from −1,000,000 to 1,000,000.
- Choose the Angle Mode. Pick degrees if your problem comes from geometry, triangles, surveying or a high-school worksheet. Pick radians if your problem comes from calculus, trig identities, physics or engineering — where angles are dimensionless.
- (Optional) Set the Power Exponent (y) if you also want x raised to a custom power, x^y. The default y = 2 simply squares x; enter y = 3 for a cube, y = −1 for the reciprocal, and so on.
- Press calculate. The result card fills in ten outputs at once: sin(x), cos(x), tan(x), the square root √x, x squared, x raised to your chosen power y, the natural log ln(x), the common log log10(x), the exponential e^x, and the factorial x factorial.
- Switch the angle mode and recalculate to compare the same number in degrees versus radians. For example, 30 in degrees gives sin = 0.5, while 30 in radians gives sin ≈ −0.988 — a reminder that the mode matters.
- Negative numbers work fine for trigonometry, squaring and powers — sin(−x) = −sin(x), after all. The functions that do not exist for negative x (square root, logarithms, factorial) simply return 0 for negative inputs instead of inventing a complex result.
A useful mental anchor: π (pi) ≈ 3.14159 radians is exactly 180 degrees, and e ≈ 2.71828 is the base of the natural logarithm.
The Functions Explained
- sin, cos, tan are the three core trigonometric ratios. Sine and cosine always stay between −1 and 1; tangent can grow without bound at 90° (π/2 radians) because it is sin divided by cos, and cos becomes zero there.
- Square root (√x) asks: "what number squared equals x?" √144 = 12, and √2 ≈ 1.4142.
- x squared (x²) is the inverse question: multiply the number by itself.
- x raised to a power y (x^y) generalizes the square: with y = 2 you get x², with y = 3 you get x³, and with y = −1 you get the reciprocal 1/x. The exponent box lets you choose y.
- Natural log (ln x) answers "to what power must e be raised to get x?" ln(e) = 1, and ln(1) = 0.
- Common log (log₁₀ x) does the same on base 10, which is why log₁₀(1000) = 3.
- Exponential (eˣ) raises e ≈ 2.71828 to the power x. It is the inverse of the natural log.
- Factorial (x!) multiplies all whole numbers from 1 up to x. By definition 0! = 1, and 5! = 1×2×3×4×5 = 120.
When a result shows 0 on purpose. Several functions have inputs where the math breaks down, and the card prints 0 in those cases as a placeholder rather than a real answer: ln(x) and log₁₀(x) for x ≤ 0 (logs need a positive number), √x for x < 0, tan(90°) (cosine is zero there), eˣ for very large x (it overflows what the engine can store), and x! for x < 0. Read those zeros as "not defined here", not as computed values.
Examples
Example 1 — One radian. With x = 1 and angle mode set to radians, sin(1) ≈ 0.8415, cos(1) ≈ 0.5403, tan(1) ≈ 1.5574, √1 = 1, x² = 1, ln(1) = 0, log₁₀(1) = 0, e¹ ≈ 2.7183 and 1! = 1. Notice that ln(1) and log₁₀(1) are both zero: the logarithm of 1 is always zero, on any base.
Example 2 — A familiar triangle angle. Switch to degrees, enter x = 30. The calculator returns sin(30°) = 0.5, cos(30°) ≈ 0.8660, tan(30°) ≈ 0.5774. These are the exact ratios of the 30-60-90 triangle. On roads, a 45° angle corresponds to a 100% grade, because tan(45°) = 1.00 — tangent directly gives the percent slope.
Example 3 — Zero. Enter x = 0. sin(0) = 0, cos(0) = 1, tan(0) = 0, √0 = 0, 0² = 0, e⁰ = 1 and 0! = 1. The factorial convention that 0! = 1 makes combinatorics formulas clean.
Example 4 — A large number. Enter x = 1,000,000 in radians. √1,000,000 = 1000, x² = 1,000,000,000,000 (one trillion), ln(1,000,000) ≈ 13.8155, and log₁₀(1,000,000) = 6. The common log being exactly 6 confirms that a million is 10 to the sixth.
FAQ
How do I switch between degrees and radians?
Use the Angle Mode selector above the calculate button. Degrees interpret x as an angle out of 360; radians interpret x in the unitless angle measure used by calculus. A full circle is 360° = 2π radians, so to convert by hand multiply degrees by π/180.
Why does tan(90°) show 0?
Tangent is sin(θ) divided by cos(θ). At 90°, cos(90°) = 0, so you are dividing by zero — mathematically tan(90°) is undefined and the true value runs off to infinity. The calculator detects cosine near zero and displays tan(x) = 0 at those points as a guard, rather than printing a meaningless huge number. Treat that 0 as "undefined here", not as a real tangent.
Do the sine/cosine/tangent results carry units?
The trig results themselves are plain ratios (sin(30°) = 0.5 with no unit). What changes with the selector is how x is read: in degrees mode enter angles like 30, 90, 180 (think of them as degrees); in radians mode enter angles like 1, π/2 ≈ 1.5708, 6.283 (unitless). The numbers on the result card are just values; a "°" would be wrong in radian mode, so the card does not append it.
What is the difference between ln and log?
On this page ln is the natural logarithm with base e ≈ 2.71828, used in calculus, growth and decay. log₁₀ is the common logarithm with base 10, used in orders of magnitude, decibels and pH. They are related by ln(x) = log₁₀(x) × ln(10).
What does e to the x (eˣ) mean?
It raises the mathematical constant e ≈ 2.71828 to the power x. It models continuous growth — compound interest, population growth, and radioactive decay. e⁰ = 1 and e¹ ≈ 2.7183.
What is a factorial and why is 0! equal to 1?
x! multiplies every integer from 1 to x: 5! = 120, 6! = 720. The convention 0! = 1 keeps combinatorics consistent — choosing zero items from a set is exactly one way. Factorials grow extremely fast: 10! = 3,628,800. This calculator gives the exact value for whole numbers from 0 through 10; larger whole numbers would overflow ordinary display limits, so the result is held at 10!, and factorials of negative numbers are shown as 0.
What happens when x is negative?
Trigonometry, squaring and powers handle negative numbers naturally: sin(−30°) = −0.5, (−7)² = 49. The functions that are undefined on the negative side of the real number line — the square root, the logarithms, and the factorial — return 0 for negative x, so you never build on a meaningless complex value. If you actually need a complex square root, use a computer algebra system.
Disclaimer
This scientific calculator is provided for informational purposes only and does not constitute mathematical, engineering, or academic advice. Outputs are computed with standard double-precision floating-point routines and are rounded to four decimal places for display; results may differ slightly from handheld devices in the last digits. Always verify critical calculations with a primary source or qualified professional.