Scientific Calculator

Order of operations on a scientific calculator

The calculator works an expression in the same order as a math class, from the first step to the last:

1. Parentheses — innermost first.
2. Factorial, percent and powers — 5!, 50%, 3², 2^10. Stacked powers go right to left.
3. A minus sign in front — −3² is −(3²).
4. Multiplication and division, left to right — including a number written next to another, like 2π or 3(4).
5. Addition and subtraction, left to right.

So 2 + 3 × 4 = 14 and 18 ÷ 6 + 4(5 − 2) = 3 + 12 = 15, as in OpenStax Prealgebra (Example 2.10). Under every answer, Read as shows the expression with all its parentheses written out — 1/2π reads as (1 ÷ 2) × π, which is π/2. If you meant 1 ÷ (2π), type the parentheses.

Missing closing parentheses at the end are added for you, and the answer says so.

Is −3² equal to 9 or −9?

The exponent belongs to the number right under it, so a minus in front is applied afterward. Textbooks agree — OpenStax Prealgebra contrasts (−2)⁴ = 16 with −2⁴ = −16 (Example 3.52). Some button calculators square whatever is already on the display, so pressing − 3 x² gives 9 there; on this calculator the Read as line removes the doubt.

Degrees or radians

A full turn is 360 degrees or 2π radians, so 180° = π radians and 1 radian ≈ 57.3°.

• Degrees — triangles, slopes, construction angles, most school geometry. sin 30 = 0.5.
• Radians — calculus, physics, anything with π in the angle. sin(π/6) = 0.5.

The same key gives a different answer in each mode: sin 30 is 0.5 in degrees and −0.988 in radians. The mode switch sits above the keypad, the screen shows DEG or RAD, and the answer notes which one was used. In radian mode, if you take the sine, cosine or tangent of a whole number like 30 or 45, the calculator also gives the answer in degrees, with a button to switch.

The inverse keys (sin⁻¹, cos⁻¹, tan⁻¹) answer in the current mode: sin⁻¹(0.5) = 30 in degrees or 0.523598775598 in radians.

Exact values of sin, cos and tan

Values from the NIST Digital Library of Mathematical Functions (Table 4.17.1). At these angles the calculator returns the exact value, so sin 180° is 0 rather than a tiny leftover such as 1.2 × 10⁻¹⁶, and tan 90° is reported as undefined instead of a huge number.

Scientific notation: the EXP key

EXP (or the letter E) means “times ten to the power”: 6.022E23 is 6.022 × 10²³, Avogadro’s number, and 1.6E−19 is 1.6 × 10⁻¹⁹. EXP binds to its number, so 6.022E23 × 0.25 = 1.5055 × 10²³.

Answers of a trillion or more, or smaller than one millionth, are shown in ×10ⁿ form. Copy puts the plain form (1.5055e23) in the summary, which spreadsheets and code understand.

Logs, roots and powers

• Other bases: log₂ 8 = ln(8) ÷ ln(2) = 3.
• Other roots: the nth root is a power of 1/n: 32^(1/5) = 2. An odd root of a negative number is real, so (−8)^(1/3) = −2.
• Compound growth: 1000(1 + 0.05/12)^(12 × 10) = 1,647.00949769 — $1,000 at 5% a year, compounded monthly for 10 years.

For percent changes, the percentage calculator explains each step, and the percent off calculator handles stacked discounts and sales tax; for exact answers with fractions, use the fraction calculator.

Keyboard shortcuts

History keeps your last 12 answers in this browser only — nothing is sent anywhere. Tap an answer to drop it into the next expression, or use Ans for the most recent one.