More than basic arithmetic
Besides plus, minus, times and divide, a scientific calculator masters a whole range of mathematical functions. They are needed at school from the middle years onwards, as well as in engineering, trades, natural sciences and financial mathematics. In the online calculator you unlock these functions with the "Scientific" mode. Here you will learn what each key stands for.
Trigonometric functions: sin, cos and tan
Sine, cosine and tangent describe side ratios in a right-angled triangle. The sine of an angle is the ratio of the opposite side to the hypotenuse, the cosine that of the adjacent side to the hypotenuse, and the tangent that of the opposite side to the adjacent side. In practice you use these functions, for example, to calculate the height of a roof from its pitch and rafter length.
An example: a 4-metre ladder leans against a wall at an angle of 70°. How high does it reach? 4 × sin(70) = 3.76 metres. For roof calculations with pitch, area and rafter length there is also the specialised roof calculator.
DEG or RAD: the most important switch
Angles can be given in degrees (DEG) or radians (RAD). A full circle is 360 degrees or 2π radians, a right angle 90 degrees or π/2. The angle mode determines how the calculator interprets your input. In DEG mode sin(30) = 0.5; in RAD mode 30 is read as radians and the result is about −0.988.
Wrong results with trigonometric functions almost always have this cause. School and everyday life mostly use degrees, physics and calculus often radians. The current mode is shown at the top left of the display.
Inverse functions: sin⁻¹, cos⁻¹ and tan⁻¹
The inverse functions answer the question of which angle belongs to a certain ratio. If a ramp rises by 1 metre over a length of 10 metres, the angle of inclination is tan⁻¹(1 ÷ 10) = 5.71°. sin⁻¹ and cos⁻¹ are only defined for values between −1 and 1. For other inputs the calculator reports an error. For slopes in percent and degrees the slope calculator is also useful.
Logarithms: ln and log
The logarithm is the inverse of the power. log stands for the common logarithm to base 10: log(1000) = 3, because 10³ = 1000. ln is the natural logarithm to base e ≈ 2.71828. It appears in growth and decay processes, such as continuously compounded interest, radioactive decay or a cup of tea cooling down.
An application: how many years does it take for capital to double at 5% interest? ln(2) ÷ ln(1.05) = 14.21 years. Logarithms are only defined for positive numbers; ln(0) or log(−1) lead to an error message. How capital develops with compound interest year by year is shown by the compound interest calculator.
Exponential functions: e^x and 10^x
The e^x and 10^x keys are the counterparts of ln and log. e^(ln(5)) gives 5 again. With 10^x you can write very large or small numbers conveniently: 3 × 10^8 is the speed of light in metres per second, 1.6 × 10^(−19) the elementary charge.
Further functions at a glance
x^y calculates any power, x² and x³ the square and cube. √ and ∛ stand for square root and cube root. 1/x forms the reciprocal. n! is the factorial, the product of all natural numbers up to n: 5! = 1 × 2 × 3 × 4 × 5 = 120. It is needed in probability, for example for the number of possible orderings. |x| returns the absolute value, i.e. the value without its sign.
The constants π ≈ 3.14159 and e ≈ 2.71828 are inserted with a key. The area of a circle with a radius of 3 metres is π × 3² = 28.27 square metres. The "Ans" key carries the last result into a new calculation.
Precision
The calculator works internally with high precision and displays 12 significant digits. Values such as sin(180°), cos(90°) or tan(45°) are returned exactly as 0, 0 and 1, without rounding leftovers. For school, university and work this precision is more than sufficient.