When you count normally, you use ten digits: 0 through 9. When you run out of digits, you start a new column — so after 9 comes 10, meaning “one ten and zero ones.” This is called base 10, and we use it because humans have ten fingers.
But ten is not the only choice. A computer uses only two states — on and off — so it counts with just two digits, 0 and 1. That is called base 2, or binary. After 1, the next number is 10 — meaning “one two and zero ones” — which equals 2 in our normal counting.
Each base has its own set of digits. Base 10 uses 0–9. Base 2 uses 0–1. Base 16 (called hexadecimal, used in computers and color codes) uses 0–9 and then A=10, B=11, C=12, D=13, E=14, F=15. This calculator goes all the way up to base 36, using every digit 0–9 and every letter A–Z.
1. Set your base at the top using the number box and Set Base, or tap one of the quick buttons: Bin 2, Oct 8, Dec 10, Hex 16, or Fun 36. The active base lights up green.
If there is already a plain number in the Input box when you switch base, it will automatically be converted to the new base. For example, if you have 15 in the box and switch to base 16, it changes to F — the same value, just written in the new base.
2. Type your math problem in the Input box. You can use + - * / for add, subtract, multiply, divide. You can also tap the + − × ÷ buttons in the Scientific panel to insert operators without typing. Use parentheses to group things, like (9+9)/9.
3. Press = or the Enter key to see the answer.
4. The answer appears in the Output box. If you are in a base other than 10, the base 10 equivalent appears below it in blue, so you can always check your work.
5. The small number at the bottom tells you how many digits are in the answer.
For very large or very small numbers in base 10, you can use scientific notation by typing E between the mantissa and the exponent. For example:
1E100 — means 10100 (a googol — 1 followed by 100 zeros)
1.5E6 — means 1,500,000
2.5E-4 — means 0.00025
This only works in base 10 because scientific notation is always a power of 10. In bases 15 and above, E is a valid digit (E=14), so it is treated as a number, not an exponent. In any base you can always use ^ instead — for example 10^100 means the base raised to the 100th power.
Just like a classic desktop calculator, you can repeat an operation by pressing = multiple times. Type a double operator to set it up:
2++2 then press = repeatedly → 4, 6, 8, 10… (keeps adding 2)
10--3 then press = repeatedly → 7, 4, 1, -2… (keeps subtracting 3)
2**3 then press = repeatedly → 6, 18, 54… (keeps multiplying by 3)
100//2 then press = repeatedly → 50, 25, 12.5… (keeps dividing by 2)
Press Clear to reset the repeat operation.
Some fractions never end — like 1/3 = 0.333... going on forever. This calculator detects that and shows the repeating part in brackets: 0.[3]. This means the 3 repeats forever. Try 1/7 to see a longer repeating pattern.
In base 36, the letters i and o are shown in lowercase so they cannot be confused with the digits 1 and 0.
The green bar near the top switches on 1000-digit precision. Click anywhere on the bar to toggle it ON or OFF. In normal mode you get about 12 digits, which is fine for everyday math. Turn on high precision when you need to see hundreds of digits — for example, the exact decimal expansion of π or a long repeating fraction.
The buttons sin, cos, tan, log, ln, √x, x², 1/x, x!, and x^y apply a mathematical function to whatever number is in the Input box. Press the button and the result appears immediately. The DEG/RAD button controls whether angles are in degrees or radians — DEG is the everyday setting.
5! — factorial (type the ! directly, or use the x! button)
17 mod 5 — remainder after division (= 2)
factor — finds the prime factors of a number in any base
You can also type pi or euler directly in the Input box.
A logarithm answers the question: “What power do I raise this base to in order to get that number?” For example, log(100) = 2 because 10² = 100. Log(1000) = 3 because 10³ = 1000.
Before computers, logarithms were how scientists, engineers, and navigators multiplied and divided large numbers — which would otherwise take hours by hand. The trick is that multiplying two numbers is the same as adding their logarithms, and dividing is the same as subtracting them. So instead of multiplying two huge numbers directly, you looked up their logarithms in a printed table, added the two logarithms together, then looked up the result in the table backwards to get your answer. This turned a very hard multiplication into a simple addition.
A physical tool called a slide rule did this mechanically. Two rulers slid against each other, with scales printed in logarithmic spacing, so sliding them gave you the product of two numbers instantly. Every engineer carried one before pocket calculators arrived in the 1970s.
This calculator has two logarithm buttons. log gives the base-10 logarithm, which is what printed tables used. ln gives the natural logarithm, which uses the base e = 2.71828… and is used more in mathematics and science.
Mod is short for modulo. It gives you the remainder after division — the amount left over that does not fit evenly.
For example: 17 mod 5 = 2, because 17 divided by 5 is 3 with a remainder of 2.
You use remainders all the time without thinking about it. Clock arithmetic works on remainders — after 12 o’clock comes 1, not 13, because we take the remainder after dividing by 12. Days of the week work the same way with remainders of 7. If today is Wednesday and you want to know what day it will be in 10 days, you calculate (3 + 10) mod 7 = 6, which is Saturday.
Remainders are also used in computer security and encryption, in generating repeating patterns, and in checking whether a number is even or odd — any number mod 2 gives a remainder of either 0 (even) or 1 (odd).
To use it, type your expression with the word mod between two numbers: 17 mod 5 and press =.
Try this example: Suppose you want to know what day of the week it will be 100 days from now. Today is Wednesday, which is day 3 if you count Sunday=0, Monday=1, Tuesday=2, Wednesday=3, Thursday=4, Friday=5, Saturday=6.
Type this in the calculator: (3 + 100) mod 7
Press = and you get 5, which is Friday. So 100 days from Wednesday is a Friday.
You can verify this makes sense: 100 divided by 7 is 14 weeks with a remainder of 2 days. Wednesday plus 2 days = Friday. ✓
Enter the coefficients a, b, and c and press Solve. For a linear equation (a·x + b = c) it finds x directly. For a quadratic equation (a·x² + b·x + c = 0) it finds both roots, and tells you if they are real or complex numbers.
A factorial means multiply a whole number by every whole number below it down to 1. It is written with an exclamation mark.
5! = 5 × 4 × 3 × 2 × 1 = 120
Factorials grow very fast. 10! = 3,628,800 and 20! = 2,432,902,008,176,640,000. They are used in counting problems — for example, how many different ways can you arrange 5 books on a shelf? The answer is 5! = 120 ways. Type a number and press the x! button, or type the ! directly after the number.
A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23…
Every other whole number is called composite, meaning it can be broken into smaller factors. For example, 12 = 2 × 2 × 3. Breaking a number down this way is called prime factoring, and the factor button does this automatically in whatever base you are using.
There are infinitely many prime numbers — they never run out, though they become rarer as numbers get larger.
Normally you cannot take the square root of a negative number. What number times itself gives −1? No ordinary number does. Mathematicians invented a solution: they defined a new number called i, where i = √−1. This is called an imaginary number — not because it is fake, but because it lives outside the ordinary number line.
A complex number combines a regular number and an imaginary number, written as a + bi. The part without i is called the real part, and the part with i is called the imaginary part. For example, 3 + 4i means “3 in the real direction and 4 in the imaginary direction.”
Complex numbers are rotational
The best way to picture a complex number is on a flat grid. The horizontal axis is the ordinary number line. The vertical axis is the imaginary number line. Every complex number is a point on this grid — or think of it as an arrow pointing from the center to that point.
Here is the remarkable part: multiplying by i rotates that arrow by 90 degrees. Multiply again by i and it rotates another 90 degrees. Do it four times and you are back where you started — which makes sense because i × i × i × i = i&sup4; = 1.
This means complex numbers are not just numbers — they describe rotation and circular motion. Anything that spins, oscillates, or travels in a wave can be described with complex numbers.
Used in electronics every day
Electrical engineers use complex numbers constantly. When electricity flows through a circuit, resistors slow it down in a straightforward way, but capacitors and inductors create a phase shift — the voltage and current get out of step with each other, like two dancers who are not quite in sync. This phase relationship is exactly a rotation, so engineers use complex numbers to describe it.
The combination of resistance and phase shift is called impedance, written as Z = R + Xi, where R is resistance and X is reactance. Engineers add, multiply, and divide these complex impedances the same way this calculator does in the Complex Numbers panel.
Radio and audio engineers use the same math to design filters — circuits that let some frequencies through and block others. A filter is designed by placing complex numbers called poles and zeros on the complex grid, and their positions determine exactly which frequencies pass.
Used in signal processing
Your phone processes sound, video, and radio signals millions of times per second using an operation called the Fourier transform, which converts a signal into its component frequencies. The entire calculation is built on complex numbers — every frequency in a signal is represented as a complex number whose magnitude is the volume of that frequency and whose angle is its timing.
A simple example
Suppose a voltage signal is 3 + 4i volts. The real part (3) is in phase with the reference. The imaginary part (4) is 90 degrees out of phase. The modulus — which the calculator shows — is √(3² + 4²) = 5 volts. That is the actual peak voltage you would measure. The argument is the angle, about 53 degrees, telling you how far out of phase the signal is.
This calculator computes all of this in the Complex Numbers panel. Enter the real and imaginary parts for two complex numbers, choose an operation, and press Calculate. The result shows the answer plus its modulus and argument automatically.
Base 36 uses all ten digits and all 26 letters, so every word can be treated as a number. Try typing a word in base 36 and pressing = to see its numeric value. You can share the number with a friend and let them decode it — a simple secret code!
This calculator goes up to base 36, using digits 0–9 and letters A–Z. But what if you need a higher base, like base 62? You can still do the math manually using this calculator as a tool.
The key idea is simple: in any base, the value of a number is built by multiplying each digit by its place value and adding them up.
Converting a base 62 number to base 10
In base 62, the digits are 0–9 (values 0–9), then A–Z (values 10–35), then a–z (values 36–61).
Suppose you have the base 62 number 3aB. Working from right to left:
• B = 11, in the ones place (62&sup0; = 1): 11 × 1 = 11
• a = 36, in the 62s place (62¹ = 62): 36 × 62 = 2,232
• 3 = 3, in the 3844s place (62² = 3,844): 3 × 3,844 = 11,532
Type each multiplication into the calculator and add the results:
11 + 2232 + 11532 = 13,775
So 3aB in base 62 equals 13,775 in base 10.
Converting a base 10 number to base 62
To go the other direction, repeatedly divide by 62 and collect the remainders. Use the mod key for the remainders and plain division for the quotients.
Start with 13,775:
1. 13775 mod 62 = 11 → digit is B
2. 13775 / 62 = 222 (drop the remainder) → divide this next
3. 222 mod 62 = 36 → digit is a
4. 222 / 62 = 3 (drop the remainder) → divide this next
5. 3 mod 62 = 3 → digit is 3
6. 3 / 62 = 0 → we are done
Read the digits from bottom to top: 3aB ✓
This same method works for any base — just replace 62 with whatever base you need.
For entertainment purposes only.