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+--- Thread: How to Write Your Own Equation — A 5-Step Method (/showthread.php?tid=446)
How to Write Your Own Equation — A 5-Step Method - Leejohnston - 01-08-2026
How to Write Your Own Equation — A 5-Step Method
Most people think equations are mysterious things invented by geniuses.
They’re not.
Equations are just structured descriptions of how reality behaves.
Here’s a simple 5-step method you can use to build your own equations for real-world problems.
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1) Define the outcome you want
Pick the thing you’re trying to calculate and name it.
Example:
“How long does it take to fill a bath?” → call it t.
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2) List what it depends on
Write down the inputs that obviously matter.
Bath fill time depends on:
• bath volume V
• flow rate Q
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3) Use “conservation” or “rate” thinking
Most real problems reduce to one of these ideas:
• amount = rate × time
• change = input − output
• energy, mass, or charge is conserved
This is where the structure of the equation comes from.
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4) Check units (this is your lie detector)
Units must match on both sides of the equation.
If they don’t, the equation is wrong — no exceptions.
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5) Add corrections (real-world factors)
Friction, efficiency, losses, resistance, leakage.
This is where ideal equations become realistic models.
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Example 1: Inventing an equation from scratch
Problem:
“How long does it take to fill a bath?”
Let:
• V = volume (litres)
• Q = flow rate (litres per minute)
• t = time (minutes)
Rate rule:
V = Q · t
Solve for time:
t = V / Q
Unit check:
• V in litres
• Q in litres per minute
V / Q = minutes ✅
Now make it more realistic.
Some water is lost, so only a fraction η of the flow is effective (efficiency from 0 to 1):
t = V / (ηQ)
You have just created a real-world equation.
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Example 2: A more physics-based case — stopping distance
Stopping distance depends on:
• speed v
• deceleration a
From motion physics:
v² = 2ad
Rearrange to predict distance:
d = v² / (2a)
Now add road friction:
a ≈ μg
So:
d ≈ v² / (2μg)
This turns an abstract equation into a usable real-world model.
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The meta-rule (the real secret)
Most useful equations come from just three ideas:
1) Rate × time
2) Conservation (energy, mass, momentum, charge)
3) Geometry (areas, volumes, inverse-square spreading)
If you can identify which one your problem belongs to, you can usually write the equation.