Formulas as Algorithms

A formula from mathematics or science arrives as a single line of notation. A program needs it as a sequence of steps, with every value either asked for, calculated, or already known. Getting from one to the other is a skill, and it is mostly about naming.

Take the cost of running an appliance: energy in kilowatt-hours, times the price per kilowatt-hour.

$\text{cost}=\frac{\text{watts}\times \text{hours}}{1000}\times \text{rate}$

The formula says nothing about where the numbers come from, in what order to do the arithmetic, or what to do when somebody types “eight” instead of 8. The algorithm has to.

watts = float(input("Appliance power, in watts: "))
hours = float(input("Hours used per day: "))
rate = float(input("Price per kilowatt-hour, in dollars: "))
 
kilowatt_hours = watts * hours / 1000
daily_cost = kilowatt_hours * rate
 
print(f"That appliance costs ${daily_cost:.2f} per day to run.")

Three things happened in the translation, and they happen every time:

1. Every symbol became a named variable. watts, not w. The formula’s brevity is a cost, not a feature, once it is code.
2. The middle got a name. kilowatt_hours is not in the formula, but naming it makes the line readable and gives you somewhere to look when the answer is wrong by a factor of a thousand.
3. Units were decided. Watts and hours in, dollars out. A comment or a prompt that states the unit prevents the most common wrong answer in this kind of program, which is a correct calculation of the wrong quantity.

The method, for any formula

1. Write the formula down as it is given, symbols and all.
2. List every symbol: is it input, is it calculated, or is it a constant like the 1000 above?
3. Order the calculations so nothing is used before it exists.
4. Name each intermediate value.
5. Check it by hand with one set of numbers you can verify — and keep that pair as your first test case, exactly as Writing a Test Plan describes.

Step 5 is the one students skip and professionals never do. A formula transcribed with a misplaced bracket produces plausible numbers forever, and only a hand-worked example catches it. Python follows the usual order of operations, so watts * hours / 1000 is fine — but watts * (hours / 1000) would be too, and only one of them is what you meant.

Curriculum connection

B3.2

solve common problems (e.g., calculation of hypotenuse, determination of primes, calculation of area and circumference) by applying mathematical equations or formulas in an algorithm;

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A1.3

use assignment statements correctly with both arithmetic and string expressions in computer programs;

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