Scientific Calculator
Evaluate arithmetic, powers, roots, trigonometric functions, logarithms and factorials. Enter an expression, choose degrees or radians, and press =.
Evaluate Scientific Expressions
Scientific Calculator Formula
Where:
- \(R\) β the result of this example expression
- \(\theta\) β an angle, interpreted in degrees or radians according to the selected mode
- \(a\) β the base of the power
- \(n\) β the exponent
This is an illustrative expression, not a fixed formula for every calculation. The calculator evaluates the expression you enter, applying parentheses and the usual order of operations.
Scientific Calculator β Calculation Example
Example: evaluate the default expression, sin(30) + 2^3, with the angle mode set to DEG.
\[\sin(30^\circ)+2^3=0.5+8=8.5\]
Result: 8.5, with no units unless the quantities in your expression have units.
How to use the calculator
- Enter your calculation in the Scientific expression field. You can type directly or use the keypad. For example, enter
sqrt(49) + 3^2to add a square root and a power. - Check the DEG or RAD button before using trigonometric functions. Click it to switch modes. DEG treats an angle such as
30as degrees; RAD treats it as radians. - Press = or Enter to evaluate the expression. Read the answer beside Result. To use that answer in another calculation, insert Ans into the expression.
- Use β« to delete a character or selected text, or C to clear the expression. Successful calculations appear under Recent calculations, with the angle mode used for each one.
Understanding scientific expressions
A scientific calculator combines ordinary arithmetic with functions such as sine, square root and logarithm. Enter an entire expression instead of calculating each part separately. Multiplication and division are evaluated before addition and subtraction; powers are evaluated before multiplication. Parentheses let you control the grouping. For instance, (2 + 3)^2 gives 25, while 2 + 3^2 gives 11.
Functions take an argument in parentheses: write sin(30), sqrt(49), ln(e) or log10(100). The calculator supports sin, cos, tan and their inverse functions asin, acos and atan. The inverse trigonometric functions return angles in the selected mode. Choose the mode based on your problem, not on the size of the number entered. For more work with angles and side lengths, use the Trigonometry Calculator.
The result is a numerical value, not an automatic unit conversion. If your expression adds lengths measured in metres, interpret the result in metres; if it combines quantities with different units, check that the operation is meaningful. The displayed result may be rounded, so it can differ slightly from an exact value involving \(\pi\), roots or trigonometric functions.
Syntax, limits and practical tips
- Use
^for powers,sqrt(...)for square roots,Οorpifor pi, andefor Eulerβs number. The keypadβs xΒ² and 1/x keys insert a square and a reciprocal power, respectively. - EXP inserts
Efor scientific notation. For example,2E3means \(2\times10^3=2000\). To convert numbers between notation formats, use the Scientific Notation Calculator. %divides the value immediately before it by 100. Thus200*10%gives 20, but200+10%gives 200.1; it does not add 10% of 200.- The n! key inserts
! after a value. Factorials require a non-negative integer and are limited to170!. For a dedicated factorial calculation, see the Factorial Calculator. - Square roots of negative numbers, logarithms of zero or negative numbers, division by zero, and undefined tangent angles produce an error rather than a real-number result. Check the input and angle mode if an error appears. For more detail on logarithm bases and values, use the Logarithm Calculator.
Results are displayed to about 12 significant digits, which is suitable for routine numerical work but not a substitute for exact symbolic algebra. Ans refers to the last successful calculation; an error does not replace it. Recent history lists up to 10 successful calculations.
Frequently Asked Questions
How do I evaluate a scientific calculator expression by hand?
Work from the innermost parentheses outward, then evaluate functions and powers before multiplication, division, addition, and subtraction. For example, in 3 + 4 Γ sqrt(9) β 2^3, calculate sqrt(9) = 3 and 2^3 = 8 first. The expression becomes 3 + 4 Γ 3 β 8 = 7.
How do I convert between degrees and radians?
Multiply degrees by \(\pi/180\) to get radians, or multiply radians by \(180/\pi\) to get degrees. For example, \(90^\circ=\pi/2\) radians. These are two units for the same angle, not two different angles. Convert your input if a problem gives an angle in one unit but you want to calculate in the other mode.
How can I calculate a logarithm with a base other than 10 or e?
Use the change-of-base rule: \(\log_b(x)=\ln(x)/\ln(b)\). You can also use \(\operatorname{log10}(x)/\operatorname{log10}(b)\). For example, enter ln(8)/ln(2) to get \(\log_2(8)=3\). The argument must be positive, and the base must be positive and different from 1.
Why do -2^2 and (-2)^2 give different answers?
Parentheses determine whether the minus sign belongs to the base. By the usual order of operations, \(-2^2\) means \(-(2^2)=-4\), while \((-2)^2=4\). When raising a negative number to a power, enclose the base in parentheses. A negative base raised to a fractional power may not have a real-number result.
Can I leave out the multiplication sign?
In some cases, yes: expressions such as 2Ο and 3(4 + 5) are interpreted as multiplication. For clarity, use * when an expression could be mistaken for a number or function name. In particular, 2E3 is scientific notation for 2000, not 2 multiplied by e multiplied by 3.
Why doesn't asin(sin(150)) return 150 degrees?
Inverse sine returns its principal value, between \(-90^\circ\) and \(90^\circ\) in DEG mode. Since \(\sin(150^\circ)=\sin(30^\circ)\), asin(sin(150)) returns 30, not 150. Many angles share the same sine, so an inverse trigonometric function cannot recover the original angle without more information.