The Physics Equation That Explains Why Running Faster is So Hard (E=mc²)

January 20, 2026 | By DLake

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The faster you want to run, the more expensive it gets—and I’m not talking about shoes.

Einstein had this formula. It’s E=mc². Short hand for energy equals mass times the speed of light squared.

Here’s why that matters for running: That “squared” part means speed is expensive. Like, really expensive.

Going a little bit faster doesn’t cost a little more energy; it costs exponentially more.

This is true physics: When you’re moving, the energy required increases with the square (two to the 2nd power) of your velocity.

So, going from 8 min pace to 7 min pace? That’s not 12.5% more effort—it’s 31% more. The math doesn’t lie. Your body knows this, and that’s why those last 30 seconds of a best time in a 5k race feel harder than the entire first half of the race.

But here’s where (I think at least) it gets interesting.

This same principle applies to training. Not just literally (moving faster costs more), but in how you improve.

New to running? You just add volume (time plus distance). Boom, you get faster. That’s easy math and linear returns.

But then you hit a wall, and more miles don’t work anymore. Now you need everything else (the 1% variables).

• Sleep
• Recovery
• Strength training
• Mobility work
• Nutrition dialed in
• Recovery protocols
• Mental game
• Periodization
• The tempo runs AND the easy runs AND the long runs AND the intervals

You’re not adding anymore, but instead you’re now multiplying.

Quick Maths: 1% better sleep × 1% better nutrition × 1% better strength work × 1% better pacing = an actual improvement.

Because speed has a tax, and the faster you want to go, the more you gotta pay.

The runners who understand this keep stacking variables. The ones who don’t just keep adding more training load (intensity x distance x time) and wonder why they’re stuck.