01-08-2026, 01:43 PM
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.
⸻
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.
⸻
2) List what it depends on
Write down the inputs that obviously matter.
Bath fill time depends on:
• bath volume V
• flow rate Q
⸻
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.
⸻
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.
⸻
5) Add corrections (real-world factors)
Friction, efficiency, losses, resistance, leakage.
This is where ideal equations become realistic models.
⸻
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.
⸻
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.
⸻
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.
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.
⸻
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.
⸻
2) List what it depends on
Write down the inputs that obviously matter.
Bath fill time depends on:
• bath volume V
• flow rate Q
⸻
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.
⸻
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.
⸻
5) Add corrections (real-world factors)
Friction, efficiency, losses, resistance, leakage.
This is where ideal equations become realistic models.
⸻
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.
⸻
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.
⸻
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.