How to use the scientific calculator
- Choose Deg or Rad. This only affects the trigonometric functions and their inverses.
- Build the calculation with the keys or type it. Function keys insert the name and an opening parenthesis, such as
sin(; type the argument and close the parenthesis, or leave off the final one and it will be added for you. - The result appears under the calculation as you type. Press = or Enter to keep it; it is also stored as Ans for the next calculation.
- Press Inv to switch eight keys to their inverse functions, and press it again to switch back.
Digits and operators work from the keyboard anywhere on the page. To type function names such as sqrt, log2 or sinh, click into the display first.
What the keys do
| Key | Function | With Inv |
|---|---|---|
| sin, cos, tan | Sine, cosine, tangent in the chosen angle unit | sin⁻¹, cos⁻¹, tan⁻¹ |
| ln | Natural logarithm (base e) | eˣ |
| log | Common logarithm (base 10) | 10ˣ |
| √ | Square root | ∛ (cube root) |
| x² | Square | x³ |
| xʸ | Power, typed as ^ | ʸ√x: 27^(1/3) = 3 |
| 1/x | Reciprocal, inserted as ^(−1) | – |
| |x| | Absolute value | – |
| x! | Factorial of a whole number from 0 to 170 | – |
| EXP | Times ten to the power: 6.02E23 | – |
| Ans | The last result | – |
A few more functions can be typed but have no key: the hyperbolic sinh, cosh and tanh, log2 (base 2), exp, cbrt, sqrt and abs.
Degrees or radians?
A full turn is 360 degrees or 2π radians, so 180° = π rad and one radian is about 57.2958°. To convert, multiply degrees by π/180 or radians by 180/π. Use Deg for angles from a protractor, a map or a building plan, and Rad for calculus and physics formulas where angles come out of other quantities, such as angular frequency.
The setting changes the answer: sin(30) is 0.5 in Deg, but −0.988031624093 in Rad, because then it means 30 radians – almost five full turns. Inverse functions return angles in the chosen unit, so sin⁻¹(0.5) gives 30 in Deg and 0.523598775598 (π/6) in Rad.
Order of operations and notation
- Powers come before multiplication and division, which come before addition and subtraction. Stacked powers are worked out from right to left:
2^3^2= 2⁹ = 512. - A minus sign in front applies after the power:
-3^2= −9, while(−3)^2= 9. - Multiplication signs can be left out:
2π,3(4 + 1)and2sin(30)all work. - Lowercase
eis Euler’s number (2.71828…), while the EXP key types a capitalE, which means “× 10 to the power” and only works straight after a number.1.5E3is 1,500, but1e3is read as 1 × e × 3 ≈ 8.155. %divides by 100, and after + or − it takes a percentage of the value in front, as on the basic calculator.
Worked examples
- Hypotenuse: a right triangle with sides 3 and 4 has a long side of
√(3² + 4²)= 5. - Height of a tree (Deg): standing 20 m from the trunk, you measure 35° up to the top.
20 × tan(35)= 14.0041507642, so the top is about 14 m above eye level. - Slope of a ramp (Deg): a ramp that rises 1 unit for every 12 along has an angle of
atan(1/12)(the tan⁻¹ key) = 4.76364169073, or about 4.76°. - Growth over time: 1,000 growing by 5% a year for 10 years becomes
1000 × 1.05^10= 1,628.89462678. The Compound Interest Calculator does this year by year, with regular deposits. - Counting combinations: the number of different five-card hands from a 52-card deck is
52! ÷ (5! × 47!)= 2,598,960. - pH: a hydrogen-ion concentration of 3.2 × 10⁻⁵ mol/L gives
−log(3.2E−5)= 4.49485002168, a pH of about 4.49.
Errors and accuracy
You get an error message instead of a result when the calculation is incomplete – an operator with nothing after it, or a parenthesis that doesn’t match – or when the answer is undefined or not a real number: division by zero, the logarithm of zero or a negative number, the square root of a negative number, sin⁻¹ of a value above 1, tan(90°), or the factorial of a fraction or of a number above 170.
Numbers are stored with about 15–17 significant digits and shown rounded to 12. Values that should be exactly zero, such as sin(180°), are shown as 0 instead of a tiny leftover like 1.2e-16. Results of 10¹⁵ or more, or smaller than 10⁻⁹, are shown in scientific notation: 170! appears as 7.25741561531e306.
FAQ
Why is sin(30) not 0.5?
The calculator is set to radians, where 30 means 30 radians. Switch to Deg.
Why does tan(π/2) give a huge number in radians instead of an error?
π can only be stored approximately, so the angle is a tiny fraction away from exactly π/2, and its tangent is very large but finite: 1.63312393532e16. In degree mode, tan(90) is recognised exactly and gives an error.
How do I calculate other roots?
Use a fractional power: the fourth root of 81 is 81^(1/4) = 3. The ʸ√x key under Inv types ^(1/ for you.
Can it work with fractions, complex numbers or statistics?
No. Results are decimal numbers, calculations whose result would be a complex number show an error, and there are no statistics or equation-solving functions. For everyday sums, the simpler Calculator has larger keys and the same history.