Welcome to the HP-15C!
The HP-15C is a legendary programmable scientific calculator that uses Reverse Polish Notation (RPN). This tutorial will teach you how to master this powerful calculator.
1. Understanding RPN (Reverse Polish Notation)
Unlike traditional calculators, RPN doesn't use an equals key. Instead, you enter numbers first, then the operation.
Example: Calculate 2 + 3
- Press 2
- Press ENTER (pushes 2 onto the stack)
- Press 3
- Press +
- Result: 5 appears in the display
The ENTER key separates numbers. Think of it as "confirming" the first number before entering the second.
2. The RPN Stack
The HP-15C has a 4-level stack (X, Y, Z, T registers). The display shows the X register.
Stack Operations:
- ENTER - Pushes X into Y, duplicates X
- R↓ - Rolls stack down (X→T, Y→X, Z→Y, T→Z)
- x⇄y - Swaps X and Y registers
- CLx - Clears X register only
Example: Calculate (2 + 3) × 4
- 2 ENTER 3 + → Display shows 5
- 4 × → Display shows 20
3. Using Prefix Keys (f and g)
Many keys have three functions:
- White text - Direct press (main function)
- Orange text (top) - Press f first
- Blue text (bottom) - Press g first
Example: Calculate x²
To square a number (orange label x² above √x button):
- Enter number: 5
- Press f (activates orange functions)
- Press √x (executes x²)
- Result: 25
Example: Calculate natural log (LN)
To get LN (blue label below e^x button):
- Enter number: 10
- Press g (activates blue functions)
- Press e^x (executes LN)
- Result: 2.3026
4. Scientific Functions
Trigonometry:
- SIN, COS, TAN - Trig functions
- f SIN - Arc sine (SIN⁻¹)
- f 7 - Set DEG mode
- f 8 - Set RAD mode
- f 9 - Set GRD mode (gradians)
Logarithms:
- 10^x - Ten to the power of x
- g 10^x - LOG (base 10)
- e^x - e to the power of x
- g e^x - LN (natural log)
Example: Calculate sin(30°)
- f 7 - Set to DEG mode
- 30 SIN
- Result: 0.5
5. Memory Storage
The HP-15C has 20 storage registers (R0-R19).
Store and Recall:
- STO 0 - Store X in register 0
- RCL 0 - Recall from register 0
Example: Store π and use it
- f EEX - Enter π (3.14159...)
- STO 1 - Store in R1
- 5 ENTER - Enter 5
- RCL 1 - Recall π
- × - Multiply by π
- Result: 15.7080 (5π)
6. Programming Basics
The HP-15C can store and execute programs!
Creating a Simple Program:
Example: Program to double a number
- f PRGM - Enter program mode
- f LBL A - Create label A
- 2 × - Multiply by 2
- g RTN - Return
- f PRGM - Exit program mode
To use: Enter a number, press GSB A
Advanced Program Example:
Example: Calculate e using Taylor Series
This program estimates e (2.71828...) using the series: e = 1 + 1/1! + 1/2! + 1/3! + ... + 1/n!
Input: Number of terms (n) in X register
Output: Estimate of e
Program steps:
- f PRGM - Enter program mode
- f LBL B - Create label B
- STO 0 - Store n in R0
- 1 - Start with 1 (for e)
- STO 1 - Store sum in R1
- 1 - Start factorial at 1
- STO 2 - Store factorial in R2
- 1 - Counter starts at 1
- STO 3 - Store counter in R3
- f LBL 0 - Loop start
- RCL 3 - Recall counter
- RCL 2 - Recall factorial
- × - Multiply (factorial = factorial × counter)
- STO 2 - Store new factorial
- 1 - Put 1 in X
- x⇄y - Swap to get factorial in X
- ÷ - Calculate 1/factorial
- RCL 1 - Recall sum
- + - Add to sum
- STO 1 - Store new sum
- RCL 3 - Recall counter
- 1 + - Increment counter
- STO 3 - Store counter
- RCL 0 - Recall n
- RCL 3 - Recall counter
- g x≤y - Test if counter ≤ n
- GTO 0 - If true, loop back
- RCL 1 - Recall final sum
- g RTN - Return
- f PRGM - Exit program mode
To use:
- Enter 5 GSB B → Result: ~2.7167 (5 terms)
- Enter 10 GSB B → Result: ~2.7183 (10 terms)
- Enter 15 GSB B → Result: 2.71828183 (excellent approximation!)
How it works:
- R0 stores the target number of terms (n)
- R1 accumulates the sum (e estimate)
- R2 tracks the factorial (1!, 2!, 3!, ...)
- R3 is the loop counter (1, 2, 3, ...)
- Each iteration adds 1/n! to the sum
- Loop continues while counter ≤ n
Programs are stored in memory and execute automatically. Use labels (A-E, 0-9) to organize multiple programs. This Taylor series example demonstrates loops, conditionals, and register management!
7. Statistics Functions
Perfect for data analysis!
Basic Statistics:
- Σ+ - Add data point (X and Y if needed)
- g Σ+ - Remove data point (Σ−)
- g 0 - Mean (x̄)
- g • - Standard deviation (s)
Example: Calculate mean of 10, 20, 30
- 10 Σ+
- 20 Σ+
- 30 Σ+
- g 0 - Calculate mean
- Result: 20
8. Common Calculations
Percentage Calculations:
What is 15% of 200?
- 200 ENTER
- 15
- f %
- Result: 30
Powers and Roots:
Calculate 2^8
- 2 ENTER
- 8
- y^x
- Result: 256
9. Quick Tips
- Clear everything: ON resets the calculator
- Fix decimals: f 7 for 7 decimal places (or any 0-9)
- Scientific notation: f 8 enables SCI mode
- Undo last entry: ← (backspace)
- Chain calculations: No need to press ENTER between operations
Practice makes perfect! RPN becomes intuitive once you get used to thinking "operands first, operation second."
10. Practice Exercises
Exercise 1: Basic Arithmetic
Calculate: (15 + 25) ÷ 8
Answer: 5
Exercise 2: Scientific
Calculate: √(25 + 144)
Answer: 13
Exercise 3: Complex
Calculate: (5² + 3²) ÷ 2
Answer: 17
Try these exercises on the calculator! Understanding how to break down complex expressions into RPN steps is key to mastering the HP-15C.