What this tool does
A scientific calculator adds trigonometry, logarithms, roots, powers and factorials to ordinary arithmetic in one keyboard-ready interface. Two settings cause almost every wrong answer: the angle mode, because sine of 30 is 0.5 in degrees while 30 radians is a completely different angle, and the logarithm base, because log means base 10 and ln means base e. Both stay visible on screen so a result can be sanity-checked before it is used.
How it works
Trigonometric functions need an angle unit, and the mode decides which one is being used. In degrees, sin 30° = 0.5, cos 60° = 0.5 and tan 45° = 1, which are the values worth memorising. In radians the same functions take a plain real number, so sin(π/6) also gives 0.5 because π/6 radians is the same angle as 30°, while entering 30 in radian mode gives about minus 0.988 because 30 radians is nearly 1,719 degrees.
Logarithms ask for a base whether or not the button says so: log is base 10, ln is base e (about 2.718), and log 1000 = 3 because 10³ = 1000. Roots are exponents written as fractions, since a square root is the one-half power and a cube root is the one-third power, so 8^(1/3) = 2. Factorials multiply an integer by every smaller positive integer, and 5! = 5 × 4 × 3 × 2 × 1 = 120, with the convention that 0! = 1.
Expressions are evaluated in the standard order: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction. That means 2 + 3 × 4 is 14 rather than 20, and 12 ÷ 3 ÷ 2 reads left to right as 2 rather than 8. Results too large or too small to read comfortably are printed in exponent notation, so 6.02e23 means 6.02 × 10²³ and keeps scientific answers precise.
Worked example
Evaluating sin 30° + 5! ÷ 10 with the angle mode set to degrees.
- Angle mode = degrees, so sin 30° = 0.5
- 5! = 5 × 4 × 3 × 2 × 1 = 120
- Multiplication and division before addition: 120 ÷ 10 = 12
- 0.5 + 12 = 12.5
The expression equals 12.5. In radian mode sin 30 ≈ -0.988, so the same keystrokes would give about 11.01.
Accuracy and limitations
- Factorials are defined only for non-negative integers and stop near 170, because larger values exceed the biggest representable floating-point number.
- Results use double-precision floating point, so trigonometric values can be off by a tiny rounding error in the last displayed digit.
- Angle and log base defaults vary between calculators and exams, so confirm which mode your course requires before trusting a figure.
Frequently asked questions
- What is the difference between degrees and radians?
- A degree splits a circle into 360 parts while a radian splits it into 2π parts, and 180° equals π radians. In degree mode sin 30° = 0.5, but the number 30 in radian mode means 30 radians, about 1,719 degrees, where sine is roughly minus 0.988. Always check the mode before reading a trigonometry result.
- What does log mean on a calculator?
- Log is base 10 and ln is base e, so log 1000 = 3 while ln 1000 is about 6.9078. For any other base use the change of base rule, such as log base 2 of 8 being log 8 divided by log 2, which equals 3.
- How do you calculate a factorial?
- Multiply the integer by every positive integer below it, so 5! = 5 × 4 × 3 × 2 × 1 = 120. By convention 0! also equals 1, because there is exactly one way to arrange nothing. Factorials are defined only for whole numbers of 0 or more.
- In what order does the calculator evaluate an expression?
- It uses standard precedence: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction. So 2 + 3 × 4 equals 14 rather than 20, because the multiplication runs before the addition.
- Is this scientific calculator free to use online?
- Yes, it runs entirely in your browser with no signup, download or account, and it keeps working offline once the page has loaded. Nothing you type is sent to a server.
- Can I use the keyboard instead of clicking buttons?
- Yes, digits, operators, parentheses and Enter are all mapped to keys, which is much faster than tapping when you are typing a full expression. Use the mode toggle whenever you switch between degrees and radians.