Scientific Calculator

Expressions are evaluated using the standard PEMDAS/BODMAS order: Parentheses first, then Exponents, then Multiplication and Division (left to right), then Addition and Subtraction (left to right).

For example, 3 + 4 × 2² evaluates the exponent first (2² = 4), then the multiplication (4 × 4 = 16), then the addition (3 + 16 = 19) — not left-to-right blindly, which would give the wrong answer of 14.

Exponents raise a base to a power (x^n means x multiplied by itself n times); roots reverse that operation (the square root of x is the number that, multiplied by itself, gives x). Logarithms answer "to what power must the base be raised to get this number?" — log₁₀(1000) = 3 because 10³ = 1,000.

Natural logarithm (ln) uses base e ≈ 2.71828 instead of base 10, and is common in calculus, finance, and growth-decay models. You can convert between any log base using the change-of-base formula: log_b(x) = ln(x) ÷ ln(b).

Sine, cosine, and tangent relate an angle in a right triangle to the ratios of its sides, and extend naturally to all real angles via the unit circle. The most important setup detail is angle mode: results differ completely depending on whether an angle is interpreted in degrees or radians.

A full circle is 360 degrees or 2π radians, so to convert degrees to radians, multiply by π ÷ 180; to convert radians to degrees, multiply by 180 ÷ π. Always confirm your calculator’s current angle mode before trusting a trig result, since this is one of the most common sources of "wrong answer" confusion.

Floating-point arithmetic on any digital calculator can introduce tiny rounding artifacts, especially near subtraction of nearly equal large numbers or very large exponentials. These artifacts are usually far smaller than the precision your real-world measurement supports, so they rarely matter in practice.

As a rule of thumb, round your final answer to match the least precise measurement that went into the calculation — reporting more decimal places than your inputs justify implies a false sense of accuracy.

Scientific notation expresses a number as a value between 1 and 10 multiplied by a power of ten, which makes extremely large or small quantities far easier to read and compare. For example, the distance from Earth to the Sun, about 150,000,000 km, is written more compactly as 1.5 × 10⁸ km, while a typical bacterium’s size might be expressed as 2 × 10⁻⁶ metres.

Multiplying numbers in scientific notation is straightforward: multiply the decimal parts together and add the exponents. Dividing works similarly but subtracts the exponents. This structure is exactly why scientific and engineering calculators expose a dedicated exponent (EXP or ×10ˣ) key rather than requiring you to type out long strings of zeros.

When checking textbook answers, enter the expression with the same parentheses the book shows, then simplify only after you confirm the calculator matches the expected intermediate steps. That habit catches both typing mistakes and formula misunderstandings.

For multi-step science problems, compute one piece at a time and write the intermediate result down. Jumping straight to a nested expression is faster, but a single misplaced parenthesis can invalidate the whole chain.

For dedicated geometry area work, the Triangle Calculator is faster than rebuilding Heron’s formula by hand here, and for ratio or markup problems the Percentage Calculator keeps the arithmetic focused on that one question.