RPN family

RPN Scientific 15 quick reference

RPN Scientific 15 is a scientific calculator that uses RPN (reverse Polish notation): you enter the numbers first, then press the operation. A four-level stack holds your numbers, so 3 ENTER 4 + gives 7 with no brackets and no equals key. It also has a solver, numeric integration, statistics and keystroke programming.

Main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register. · Shift layer: f · Second layer: g

Open in Trident

Keys

Menus and screens

The stack (X, Y, Z, T)

Four registers. The display shows X. ENTER copies X up one level; R↓ rolls the stack and x⇄y swaps X and Y.

Registers

STO and RCL save and recall numbers in registers 0-9, .0-.9 and I. Add + − × ÷ after STO or RCL to do arithmetic on a register.

Program mode

g then R/S switches program mode on and off. In program mode, the keys you press are recorded as program steps instead of being run.

Matrices and complex numbers

These parts of the original are not included in this model yet; those keys show an error.

Modes and settings

FIX / SCI / ENG

f then 7, 8 or 9 then a digit 0-9 sets fixed, scientific or engineering display with that many decimals. The default is FIX 4.

Angle mode

g then 7, 8 or 9 chooses degrees, radians or gradians for trig. The default is degrees.

USER mode

f then RCL toggles USER mode, where the top-row keys A-E run program labels directly.

Flags

g then 4 sets a flag, g then 5 clears it, and g then 6 tests it. Use them in programs for yes/no decisions.

Tips

• Press ENTER only to separate two numbers typed one after the other. After a result, you can start typing a new number directly.
• Work from the inside out: for (3 + 4) × 5, press 3 ENTER 4 + 5 ×.
• LSTx (g then ENTER) brings back the number that was in X before the last operation. It is handy for fixing mistakes.
• For SOLVE and ∫xy, first write a program with a label, then call it with f then ÷ or f then ×.
• The back arrow only fixes a number being typed; after a result it clears X.
• The display mode (FIX 4, and so on) changes only what you see. The calculator keeps more digits inside.

Guides for this calculator

• Do basic arithmeticAdd, subtract, multiply and divide, and see how each calculator family shows the answer.
• Use brackets to control the orderGroup part of a calculation with brackets so it is worked out first.
• Enter and calculate with negative numbersUse the negative-sign key (not the subtract key) so a number really becomes negative.
• Powers and exponentsSquare a number or raise it to any power such as 2 to the 10th.
• Find a square rootGet the square root of a number, exactly or as a decimal.
• Cube roots and other rootsFind any root of a number, such as the cube root of 27.
• Find a percentage of a numberWork out 15% of 200 with the percent key or by dividing by 100.
• Reuse the last answerCarry the previous result into your next calculation without retyping it.
• Store a number in a variableSave a value under a letter so you can use it again in later calculations.
• Evaluate an expression for a value of xFind the value of 3x² − 2x + 1 when x is 4.
• Solve a linear equationFind x in an equation like 3x + 5 = 20.
• Absolute valueFind how far a number is from zero, ignoring its sign.
• Round answers to a set number of decimalsChange the display so every answer shows, say, 2 decimal places.
• Use the Pythagorean theoremFind the long side (hypotenuse) of a right triangle from the two shorter sides.
• Distance between two pointsFind how far apart two points are on a graph, using the distance formula.
• Find the slope of a lineWork out rise over run between two points, such as (2, 1) and (6, 4).
• Area of a circleUse A = πr² to find the area of a circle with radius 5.
• Area of a triangleFind a triangle area from base and height, or from three side lengths with Heron's formula.
• Volume of a cylinderUse V = πr²h for a cylinder with radius 3 and height 10.
• Volume of a sphereUse V = (4/3)πr³ for a sphere with radius 6.
• Volume of a coneUse V = (1/3)πr²h for a cone with radius 3 and height 7.
• Surface area of a boxAdd the area of all six faces of a rectangular box (8 by 5 by 3).
• Angles in a polygonFind the sum of the inside angles and the size of each angle in a regular polygon.
• Degrees, minutes and secondsConvert an angle between decimal degrees (35.5125) and degrees-minutes-seconds (35°30'45").
• Set degrees or radiansTell the calculator whether angles are measured in degrees or radians before you use sin, cos or tan.
• Find sine, cosine and tangentGet sin, cos or tan of an angle, here sin 50, cos 50 and tan 50 in degrees.
• Find an angle from a ratioUse the inverse trig functions (sin⁻¹, cos⁻¹, tan⁻¹) to turn a ratio back into an angle.
• Convert between degrees and radiansChange an angle from degrees to radians and back with the calculator.
• Solve a right triangleFind a missing side from the hypotenuse and an angle, and a missing angle from two sides.
• Use the law of sinesFind a side of any triangle when you know the opposite angle of another side and its length.
• Use the law of cosinesFind the third side of a triangle when you know two sides and the angle between them.
• Secant, cosecant and cotangentGet sec, csc and cot by taking the reciprocal of cos, sin and tan.
• Convert between polar and rectangularTurn a point (x, y) into a distance r and an angle θ.
• Check unit circle valuesFind the exact values of sin, cos and tan at 30, 45 and 60 degrees.
• Hyperbolic functionsFind sinh, cosh and tanh with the hyperbolic menu.
• Work with logarithmsFind log base 10 of a number and undo it with 10 to a power.
• Natural logs and the number eUse ln and eˣ, the natural log and its inverse, based on e ≈ 2.71828.
• Logarithm with any baseFind a log such as log base 2 of 20 by dividing two natural logs.
• Exponential growthFind what a quantity grows to at a fixed percentage rate, and how long it takes to double.
• Sum a sequence or seriesAdd up the first terms of a sequence, such as 1 + 3 + 5 + … + 19, which comes to 100.
• Solve an equation numericallyFind a root of any equation by giving a starting guess and letting the calculator home in on the answer.
• Integrate on an RPN calculatorWrite a short program for your function, then integrate it between two limits.
• Find the mean and spread of one listGet the count, sum, mean and standard deviation of a list of numbers in one go.
• Summarise paired data (x and y)Get the means, spreads and cross-product sum for two lists of numbers that go together.
• Fit a straight line to dataFind the least-squares line y = ax + b that best matches a set of points.
• Measure how strongly two lists are relatedFind the correlation coefficient r, which runs from -1 (perfect downhill) to +1 (perfect uphill).
• Find the mean, median and modeWork out the average (mean), the middle value (median) and the most common value (mode) of a list.
• Find the standard deviationMeasure how spread out a list is, using the sample or the population formula.
• Count arrangements and selections (nPr and nCr)Count how many ways to arrange or choose items from a group.
• Calculate a factorialMultiply a whole number by every whole number below it, such as 6! = 720.
• Simple interestInterest on a fixed amount that does not itself earn interest: I = P × r × t.
• Enter very big and very small numbersType numbers like 6.022 × 10²³ with the exponent key and read answers shown in scientific notation.
• Show answers in engineering notationDisplay results with powers of ten that are multiples of three, like 47 × 10³ for 47 kilo-units.
• Round an answer to significant figuresShow a result with the right number of significant figures, and see how to count them.
• Use a physical constant in a formulaEnter constants such as the speed of light correctly, store them for reuse, and see them in the Units lab.
• Convert between unitsChange miles per hour to metres per second (or any unit) by multiplying by conversion factors.
• Calculate molar massAdd up the atomic masses of every atom in a formula, like glucose C₆H₁₂O₆, to get grams per mole.
• Use the ideal gas lawFind the volume of a gas from PV = nRT, with moles, temperature and pressure.
• Calculate pH and hydrogen-ion concentrationUse the log key for pH = -log[H⁺] and the 10ˣ key to go back from pH to concentration.
• Work out radioactive decay with half-lifeFind how much of a sample is left after some time, using N = N₀ × (1/2)^(t/T).
• Use Ohm's law and parallel resistorsFind the combined resistance of two resistors in parallel and then the current from V = IR.
• Calculate kinetic and potential energyFind kinetic energy with ½mv² and gravitational potential energy with mgh.
• How the RPN stack worksEnter numbers first, then the operation. Learn what ENTER, swap and the stack do.
• Record a keystroke programStore a sequence of keys under a label and replay it with one press.
• Solve an equation with your own programWrite the equation as a program, then let SOLVE find where it equals zero.