Blinded by Units of Measure

E = mc² isn’t huge—we just made it look that way

We’ve all heard it:
E = mc² — the most famous equation in physics.
A tiny bit of mass, multiplied by the speed of light squared, yields a massive amount of energy.

That’s the story, right?
It’s supposed to be profound. Awe-inspiring.

And in one sense, it is.
The idea that mass and energy are convertible—that they’re two aspects of the same physical entity—is not obvious. It’s not intuitive. It really is a deep structural truth about how the universe works.

But the scale of it? The jaw-dropping size of the number?
That’s not a statement about the relative sizes of energy and mass in the universe—
it’s just a reflection of the values we assigned to the units we chose to use for measurement.

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How Big Is Big?

The speed of light squared is a huge number—about 90 quadrillion.
So when you multiply a mass—say, 0.0025 kilograms, the mass of a penny—by that number, you get what looks like a gigantic quantity of energy:

2.25×10¹⁴ joules = 0.0025 kg × (3×10⁸ m/s)²

People see the resulting value of energy and say:

“There’s an incredible amount of energy locked inside matter!”

But why does that number come out so “big”?

Because of how we chose to measure.

We defined distance in meters and time in seconds.
Those are just tools—human-sized units for human-scale tasks.
When we plug those into a universal equation, we get a result that looks massive—but only because the units we used chopped reality into such fine pieces.

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Now change the units, and the story changes.

If we measured the speed of light in galaxy-widths per century, the speed of light becomes:

c ≈ 0.001, and c² ≈ 0.000001

Now, plug that into the same equation with the same mass, and the resulting energy would look tiny:

2.5 × 10⁻⁹

The physics didn’t change. Only the resulting number did—because we changed the units.

There’s no such thing as a big number in isolation.
Big compared to what?
If we forget that every numeric value depends on the ruler we picked,
we mistake formatting for insight.

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The Penny and the Bomb

So why does it hit so hard?

Because of examples like this:
Take that same penny. If you could convert all of its mass into pure energy, you’d release about 50 kilotons of energy.

That’s more than the bomb dropped on Hiroshima.

Now the equation doesn’t just look impressive—
it feels massive.
A familiar object. A city-sized explosion. It catches our attention.

But that’s not because the underlying physics is somehow objectively dramatic.
It’s because our perception is shaped by the scale we live in.

You live in a body that can’t handle that much energy.
You live in a world where pennies are “small” and atomic explosions are “huge”—on your scale.
The math didn’t change.
The perspective did.

However…
To an atom, a penny is a galaxy.
To the universe, Hiroshima was a blink.

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The Actual Insight

Strip away the units.
Strip away the scale.
Here’s what E = mc² really means:

Mass and energy are convertible.
They’re not the same thing,
but they’re tied together by a fixed relationship.

The resulting value only seems big
if we mistake our formatting for insight.