Scientific Calculator
Trigonometry, logarithms and powers.
4.5
30° = 30
sin(30°) = 0.5
√(144) = 12
√(144) ÷ 3 = 4
sin(30°) + √(144) ÷ 3 = 4.5
Scientific Calculator Math Formula
A scientific calculator follows a few fixed rules. Knowing them lets you check any answer by hand. Here are the five that matter most, each worked through with real numbers.
1. Order of operations (BODMAS / PEMDAS)
Brackets → Powers and roots → × ÷ → + −
Example: 8 + 2 × (3 + 4)² ÷ 7
Brackets: 3 + 4 = 7
Power: 7² = 49
Multiply: 2 × 49 = 98
Divide: 98 ÷ 7 = 14
Add: 8 + 14 = 22
Multiplication and division share the same level and are worked left to right, as are addition and subtraction. Typing the whole expression, instead of calculating in pieces, avoids most mistakes.
2. Degrees and radians
Radians = Degrees × π ÷ 180
Example: sin(30°)
30 × π ÷ 180 = 0.5236 rad
sin(0.5236) = 0.5
The most common wrong answer comes from the wrong angle mode. In radian mode, sin(30) is -0.988, because 30 is read as 30 radians. Switch the angle unit to Deg whenever your angle is in degrees.
3. Logarithms and powers
logb(x) = ln(x) ÷ ln(b)
A logarithm answers "what power gives this number?". Example: log2(1024)
ln(1024) ÷ ln(2) = 6.9315 ÷ 0.6931 = 10
That checks out, since 210 = 1,024. The same idea gives log(1000) = 3 on the common (base 10) log, because 103 = 1,000.
4. Quadratic equations
x = (−b ± √(b² − 4ac)) ÷ 2a
Example: 2x² − 4x − 6 = 0, so a = 2, b = -4, c = -6.
Discriminant: (−4)² − 4 × 2 × (−6) = 64
√64 = 8
x = (4 + 8) ÷ 4 = 3
x = (4 − 8) ÷ 4 = -1
A positive discriminant gives two real roots, zero gives one, and a negative one gives no real roots. The Solve tab does this for you and also handles cubic and higher polynomials.
5. Mean and standard deviation
Mean = Σx ÷ n
s = √( Σ(x − mean)² ÷ (n − 1) )
Example: the data 4, 8, 6, 5, 3, 7.
Mean = 33 ÷ 6 = 5.5
Σ(x − mean)² = 17.5
Sample variance = 17.5 ÷ 5 = 3.5
s = √3.5 = 1.8708
Use n − 1 when your data is a sample of a larger group. If your data is the whole group, divide by n instead: the standard deviation is then 1.7078.
Online Scientific Calculator
Our free online scientific calculator goes well beyond a basic calculator. Type a full expression such as sin(30) + log(1000) and get the answer as you type, with the working shown step by step. It handles trigonometry in degrees, radians or grads, logarithms, powers and roots, factorials, permutations and combinations, and constants like π and e.
It also graphs functions, finds derivatives, integrals and limits, solves quadratic and other polynomial equations and systems of equations, and calculates mean, standard deviation and linear regression. It is built for students, engineers and anyone who needs more than a basic calculator, and it works on phones, tablets and desktops with no sign-up.
Features Of ToolVega Scientific Calculator
- Type whole expressions with brackets and the correct order of operations, with a live answer as you type
- Degrees, radians and grads for all trigonometric functions
- Trig, inverse trig and hyperbolic functions, logarithms, roots, powers, factorials, nPr and nCr
- Constants such as π, e and the golden ratio, plus Ans to reuse the last result
- Step-by-step working and a history of past calculations
- Normal, scientific and engineering result formats with adjustable digits
- Graph several functions, zoom and pan, trace points and find roots, peaks and intersections
- Calculus: integral, slope, limit and peaks for any function
- Solve polynomial equations, any equation for x, and systems of up to four equations
- Statistics: mean, median, standard deviation, quartiles and linear regression
- Free, no sign-up, works on phone, tablet and desktop
- Private: everything is calculated in your browser
Frequently asked questions
How do I switch between degrees and radians?
Use the Angle unit buttons above the display and choose Deg, Rad or Grad. Degrees measure a full circle as 360, radians as 2π (about 6.283) and grads as 400. The mode changes every trig answer: sin(30) is 0.5 in degree mode but -0.988 in radian mode. If a sine, cosine or tangent answer looks wrong, check the angle unit first.
What is the order of operations on a scientific calculator?
Brackets first, then powers and roots, then multiplication and division from left to right, then addition and subtraction from left to right. This is called BODMAS or PEMDAS. For example, 8 + 2 × (3 + 4)² ÷ 7 equals 22, not a larger number, because the bracket and the power are worked out before the multiplication, division and addition. Typing the full expression with brackets lets the calculator apply these rules for you.
How do I solve a quadratic equation?
Put the equation in the form ax² + bx + c = 0 and use x = (−b ± √(b² − 4ac)) ÷ 2a. For 2x² − 4x − 6 = 0 the discriminant is 64, so the roots are x = 3 and x = -1. In the Solve tab, choose Polynomial, enter the coefficients and the roots appear with the working. It also solves any equation for x and sets of up to four equations.
Should I use sample or population standard deviation?
Use the sample standard deviation (divide by n − 1) when your numbers are a sample taken from a larger group, which is the usual case in surveys, experiments and coursework. Use the population standard deviation (divide by n) only when your list is every value in the group. For the data 4, 8, 6, 5, 3, 7, the sample result is 1.8708 and the population result is 1.7078. The Statistics tab lets you pick either one.
What can this scientific calculator do besides basic maths?
It calculates trigonometric, inverse and hyperbolic functions, logarithms (ln, log, log2), powers, roots, factorials, permutations (nPr), combinations (nCr), gcd, lcm and constants such as π and e. It also graphs functions, finds integrals, slopes, limits and peaks, solves polynomial equations and systems of equations, and runs statistics including mean, median, standard deviation, quartiles and linear regression. It is free, needs no sign-up and runs in your browser, so nothing you enter is stored or sent anywhere.