Scientific Calculator: Trig, Logs, Powers and Factorials

The scientific calculator adds measured functions to the four operations: sine, cosine and tangent with their inverses and hyperbolic counterparts; logarithms in base 10, base e and base 2; powers and roots; factorial; the constants π and e; modulo, absolute value, floor and ceiling. An angle selector moves every trigonometric key between degrees, radians and gradians, and a shift key reaches the function printed second on each key. It fits triangle sides and elevation angles, decibel and pH scales, compound growth, and counts of arrangements.

Scientific Calculator: Trig, Logs, Powers and Factorials

Keys, inputs and angle mode

Digits, +, −, ×, ÷, ±, CE, C and backspace work as on the standard calculator; mod returns a remainder, and the memory row stores and recalls values.
Powers and roots: x², x³, xʸ (type the base, press xʸ, type the exponent, press =), eˣ and 10ˣ; the shift key swaps in √, ∛, ln and log; 1/x and log₂ sit on the keypad.
sin, cos and tan use the selected unit; shifted, they become asin, acos and atan, which answer in the same unit. sinh, cosh and tanh ignore the angle unit, and shift reaches their inverses.
The remaining keys: n!, |x|, ⌊x⌋ (floor), ⌈x⌉ (ceiling), and π and e; F-E toggles scientific notation.

DEG is the default, and the mode in force when a key is pressed is the one used. The same digits give different numbers: 30 then sin shows 0.5 in DEG, −0.9880316241 in RAD, and 100 then sin shows 1 in GRAD. Inverses return in the current unit: 0.5 then asin shows 30 in DEG and 0.5235987756 in RAD; 1 then atan shows 45 in DEG and 0.7853981634 in RAD. They return principal values only — asin between −90° and 90°, acos between 0° and 180° — so an obtuse solution has to be finished by reasoning about the quadrant. The trap to remember: the digits 30 mean 30° in DEG and 30 radians in RAD, and the two answers are not close.

Worked examples

Height from an elevation angle. A mast stands 25 m away and its top is 32° above the horizontal. 32 then tan shows 0.6248693519; × 25 = shows 15.6217337975. Multiplying the untouched tangent gives 15.6217337977, about 0.2 nanometres apart — far below measurement precision, but a sign that the readout is a working value.
pH from a concentration. For a hydrogen-ion concentration of 0.0025 mol/L, pH = −log₁₀(0.0025). Keys: 0.0025 then log shows −2.6020599913; ± shows 2.6020599913.
Compound growth. A quantity growing 5% a year multiplies by 1.05¹⁰: 1.05 xʸ 10 = shows 1.6288946268, and × 100 = shows 162.88946268. Over thirty years, 1.05 xʸ 30 = shows 4.3219423752 — repeated growth multiplies, rather than adding 30 × 5%.

Background

Hewlett-Packard's HP-35, introduced in 1972 for US$395 and using reverse Polish notation, was the first handheld scientific calculator; it displaced slide rules and printed function tables. Early machines computed transcendental functions with algorithms such as CORDIC. Angle units are older: the radian is the SI unit of plane angle, defined so that an arc equal to the radius subtends one radian, which makes a full turn 2π radians and one radian about 57.295779513°. Degrees divide the circle into 360 parts and remain convenient for navigation and surveying; gradians came out of metrication, with 100 gradians to a right angle and 400 to a full turn.

Reading the results, and the limits

Display rule.: Results carry at most 16 significant digits and at most 10 decimal places. π shows 3.1415926536, e shows 2.7182818285, √2 shows 1.4142135624, and sin 30 in DEG shows 0.5 even though the stored value is 0.49999999999999994.
Edge cases.: 90 then tan in DEG shows 1.6331239353e+16: the angle is represented slightly away from the pole, so the key returns a huge number rather than an error. 0 then log shows −∞, while √(−1) and acosh 0.5 put the display into an error state, and atanh 1 shows ∞. Factorials accept whole numbers from 0 to 170: 170! shows 7.2574156153e+306, while 171!, 5.5! and negative factorials are rejected. mod keeps the sign of the dividend, so −10 mod 3 shows −1, not 2.
The display carries forward.: Only the displayed number feeds the next step, and constants pass through the display like any other value. In RAD mode, π followed by sin shows 0: the constant is handed over as the rounded 3.1415926536, whose sine is about −1.0 × 10⁻¹¹, and the ten-decimal display rounds that to zero.
No plots or symbolic algebra.: It does not draw a curve or solve an equation for x; plotted relationships belong to the graphing calculator.

Common mistakes

Leaving the angle mode on the wrong unit. sin 30 is 0.5 in DEG and −0.9880316241 in RAD; check the selector before a trigonometric sequence.
Reading log as the natural logarithm. log is base 10 and ln is base e: log 1000 shows 3, ln 100 shows 4.605170186.
Reading asin as a reciprocal. asin 0.5 returns an angle (30 in DEG); 1 / sin 0.5 is a different quantity.
Expecting a friendly "undefined" from every edge case. tan 90 returns a huge number, log 0 returns −∞, and √(−1) errors.

Where it is used

Triangle sides and elevation angles. 32 then tan times a 25 m distance gives 15.6217337975 m, the mast-height route; the inverse keys turn a ratio back into an angle in the selected unit.
Logarithmic scales. pH from a concentration: 0.0025 then log, then ±, gives pH 2.6020599913; decibel ratios use the same base-10 pair, log and 10ˣ.
Growth and arrangements. Compound growth is xʸ: 1.05¹⁰ shows 1.6288946268; counts of arrangements use n!, up to the 170! limit.

Privacy

Every key press is evaluated in the browser. Inputs and memory stay on the device.

Sources

Wikipedia, Scientific calculator: https://en.wikipedia.org/wiki/Scientific_calculator （访问日期：2026-09-30）
Wikipedia, Radian: https://en.wikipedia.org/wiki/Radian （访问日期：2026-09-30）
Wikipedia, Gradian: https://en.wikipedia.org/wiki/Gradian （访问日期：2026-09-30）
Wikipedia, Factorial: https://en.wikipedia.org/wiki/Factorial （访问日期：2026-09-30）
BIPM, The International System of Units (SI Brochure): https://www.bipm.org/en/publications/si-brochure （访问日期：2026-09-30）

Sources & review

Reviewed by: CalcX Editorial Team
Updated: 2026-09-30