Scientific Calculator

DEG RAD GRAD

Calculation History

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Trigonometric Functions

The sine, cosine, and tangent functions relate angles to ratios of sides in a right triangle. This calculator supports three angle modes: degrees (the most common for everyday use), radians (standard in mathematics and physics), and gradians (common in surveying, where a right angle equals 100 gradians).

The Right Triangle Definitions

sin(θ) = Opposite / Hypotenuse cos(θ) = Adjacent / Hypotenuse tan(θ) = Opposite / Adjacent = sin(θ) / cos(θ) The 2nd key reveals inverse functions: sin⁻¹, cos⁻¹, tan⁻¹ (arcsine, arccosine, arctangent)

Common Values

Angle (°)	Radians	sin	cos	tan
0	0	0	1	0
30	π/6	0.500	0.866	0.577
45	π/4	0.707	0.707	1.000
60	π/3	0.866	0.500	1.732
90	π/2	1.000	0	undefined
180	π	0	-1.000	0

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Degrees to radians: multiply by π/180. Radians to degrees: multiply by 180/π. The radian is the natural unit for mathematics because it makes calculus formulas cleaner - the derivative of sin(x) is cos(x) only when x is in radians.

Logarithms and Exponents

A logarithm is the inverse of exponentiation. The logarithm base b of a number x answers: "to what power must b be raised to produce x?" This calculator provides two logarithm bases and their inverse operations.

log(x) = log₁₀(x) - common logarithm (base 10) 2nd → log reverses to 10^x ln(x) = logₑ(x) - natural logarithm (base e) 2nd → ln reverses to e^x (Euler's number ≈ 2.71828)

Logarithm Laws

Product: log(ab) = log(a) + log(b)
Quotient: log(a/b) = log(a) - log(b)
Power: log(aⁿ) = n × log(a)
Change of base: log_b(x) = ln(x) / ln(b) = log(x) / log(b)

Why Natural Logarithms Matter

The natural logarithm base e appears throughout science, finance, and engineering because continuous growth and decay follow e^(rt). The continuous compound interest formula A = Pe^(rt), radioactive decay N = N₀e^(-λt), and population growth models all use the natural base. When working with rates and time, ln and e are almost always the correct tools.

How to Use the 2nd Function Key

Many scientific calculator buttons serve double duty. The 2nd key (shown in blue) activates the secondary function listed at the top-right corner of each button. Press 2nd, then the function button. The small label in the corner shows what the second function does.

Primary Function	2nd Function	Example
sin	sin⁻¹ (arcsin)	sin⁻¹(0.5) = 30° (in DEG mode)
cos	cos⁻¹ (arccos)	cos⁻¹(0.866) ≈ 30°
tan	tan⁻¹ (arctan)	tan⁻¹(1) = 45°
log	10^x	10^3 = 1,000
ln	e^x	e^1 = 2.71828…
√x	x² (square)	5² = 25
∛x	x³ (cube)	4³ = 64
xʸ	ʸ√x (yth root)	Enter 27, then ʸ√x, then 3 = 3 (cube root of 27)

Memory Functions

The four memory functions let you store, retrieve, and modify a single value across multiple calculations:

MC (Memory Clear): Erases the stored memory value, resetting it to zero.
MR (Memory Recall): Inserts the current memory value into the display, ready to use in a calculation.
M+ (Memory Add): Adds the current displayed value to the stored memory. Useful for accumulating a running total.
M- (Memory Subtract): Subtracts the current displayed value from the stored memory.

The display shows an "M" indicator when a non-zero value is stored in memory. A common use: calculate a subtotal, press M+, calculate a second subtotal, press M+, then press MR to see the grand total - without writing down intermediate results.

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ANS recalls the result of the most recent complete calculation. This is faster than memory when you just need the previous answer in your next expression. For example: calculate 125/7, then immediately type × 4, and the calculator uses the prior result automatically.

Constants and Special Values

Pi (π)

Pi is the ratio of a circle's circumference to its diameter. It is irrational (cannot be expressed as a fraction) and transcendental (not the root of any polynomial with integer coefficients). The calculator stores π to full floating-point precision: 3.141592653589793.

π ≈ 3.14159265358979323846… Circumference = 2πr · Area = πr² · Sphere volume = 4/3 πr³

Euler's Number (e)

Euler's number is the base of the natural logarithm and the unique real number whose exponential function equals its own derivative. It emerges naturally from continuous compounding, probability theory, and many areas of physics.

e ≈ 2.71828182845904523536… lim(n→∞) (1 + 1/n)^n · d/dx [e^x] = e^x

EXP Button

The EXP button enters numbers in scientific notation: press 6.02 then EXP then 23 to enter 6.02 × 10²³ (Avogadro's number). This avoids typing long strings of zeros and preserves full precision for very large or very small numbers.

Order of Operations

This calculator follows the standard mathematical order of operations, which determines the sequence in which a compound expression is evaluated. Parentheses can override any default order.

The order is commonly remembered as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) or BODMAS in British English:

Parentheses ( ): Everything inside parentheses is evaluated first. Nested parentheses work from the innermost outward.
Exponents and roots: Powers and roots are evaluated next, right-to-left for stacked exponents.
Multiplication and Division: Evaluated left-to-right, at equal priority.
Addition and Subtraction: Evaluated left-to-right, at equal priority.

2 + 3 × 4 = 2 + 12 = 14 (not 20) Multiplication before addition. Use (2+3) × 4 = 20 if you mean the sum first. 8 ÷ 2(2+2) - a famously ambiguous expression Strict PEMDAS: 8 ÷ 2 × 4 = 16. Implicit multiplication interpretation: 8 ÷ (2×4) = 1. This calculator follows strict left-to-right evaluation: result = 16.

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When in doubt, use parentheses. They always produce the intended result and eliminate ambiguity. The cost of an extra pair of parentheses is zero; the cost of a wrong answer in an exam or engineering calculation can be significant.

Frequently Asked Questions

When should I use radians vs degrees?

Use degrees for geometry, navigation, and everyday angle problems where right angles are 90° and full circles are 360°. Use radians for calculus, physics, engineering, and any mathematical context involving derivatives or integrals of trigonometric functions. The derivative of sin(x) is cos(x) only in radian mode. In degree mode, you would need a conversion factor of π/180. Most computer programming languages and scientific libraries use radians by default.

What does the mod function do?

Modulo (mod) returns the remainder after division. 17 mod 5 = 2, because 17 = 3 × 5 + 2. It is used extensively in computer science (checking if a number is even: n mod 2 = 0), cryptography, and clock arithmetic. On this calculator, enter the dividend (17), press mod, enter the divisor (5), then press = to get the remainder (2).

How do I calculate a factorial?

Enter the number, then press the n! button. 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials grow extremely fast: 20! = 2,432,902,008,176,640,000. The calculator handles values up to 170! before exceeding floating-point range. Factorials are used in combinatorics: the number of ways to arrange n objects is n!, and the number of ways to choose k from n is n! / (k! × (n-k)!).

What is the difference between log and ln?

log (without a base specified) on most calculators means log base 10, the common logarithm. log(1000) = 3 because 10³ = 1000. ln is the natural logarithm, base e. ln(e) = 1 because e¹ = e. ln is used more frequently in advanced mathematics and sciences. To convert: log₁₀(x) = ln(x) / ln(10) ≈ ln(x) / 2.302585. In many programming languages, log() actually means the natural log, so always check context.

How do I enter very large or very small numbers?

Use the EXP button for scientific notation. To enter 2.5 × 10⁻⁶: type 2.5, press EXP, press +/-, type 6. The display shows 2.5e-6. This is more reliable than typing out zeros and avoids input errors. Results that exceed display width automatically switch to scientific notation. You can also use EXP in the middle of an expression: 6.02 EXP 23 × 1.38 EXP -23 gives the product of Avogadro's number and Boltzmann's constant.