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The Fundamental Equation of Running Speed
The Velocity Equation
Translation: How fast you run depends on how often your feet hit the ground (Cadence) multiplied by how far you travel with each full stride (Stride Length).
This fundamental equation governs all running performance. To get faster, you must either:
- Increase Cadence (turnover faster) while maintaining Stride Length
- Increase Stride Length (travel farther per stride) while maintaining Cadence
- Optimize both (the ideal approach for elite performance)
⚖️ The Trade-off
Cadence and Stride Length are generally inversely related. As one increases, the other tends to decrease. The art of running is finding the optimal balance for your event, body type, and current fitness level.
Cadence (Steps per Minute)
What is Cadence?
Cadence, measured in Steps Per Minute (SPM), is the total number of times your feet strike the ground in one minute. It is one of the most important metrics for both speed and injury prevention.
Formula
Example:
If you take 180 steps in a 60-second interval:
📝 Stride vs. Step
In most running analytics, Cadence refers to steps (every foot strike). A Stride technically represents a full cycle (left + right), so 180 steps = 90 strides.
Typical Cadence Benchmarks
Easy / Recovery Run
Threshold / Marathon Pace
Sprints (400m - 1500m)
🎯 The "180 SPM" Myth
Historically, 180 SPM was considered the "magic number." Modern research shows that while elite runners do stay near or above this mark, the optimal cadence is highly individual based on leg length and speed.
Interpreting Cadence
🐢 Cadence Too Low
Characteristics:
- Overstriding (foot lands far in front of center of mass)
- Significant vertical bounce (high vertical oscillation)
- Heavy landing impact and higher injury risk
Result: Braking forces—each step slows you down before you push forward again.
Fix: Increase step frequency, focus on "quick feet," land with foot under hips.
🏃 Cadence Too High
Characteristics:
- Choppy, short strides
- Insufficient hip extension and power
- High cardiovascular demand for lower speed
Result: Poor economy—you're working hard but not traveling far per step.
Fix: Targeted power work (hills), focus on a full stride cycle and push-off.
⚡ Optimal Cadence
Characteristics:
- Fluid, efficient movement
- Minimal vertical oscillation
- Quick ground contact time
- Sustainable rhythm
Result: Maximum speed with controlled impact and energy expenditure.
How to Find: Use a metronome or music at 5-10% above your baseline cadence.
Stride Length
What is Stride Length?
Stride Length is the distance traveled in one full cycle (two steps). It represents the power and mechanical efficiency of your running gait.
Formula
Or:
Example:
Running a kilometer (1000m) in 800 steps:
Stride Length = 1000 / 400 = 2.50 meters
Typical Stride Length Benchmarks
Elite Runners (2:05 Marathon)
Competitive Runners
Fitness Runners
Beginners
📏 The Height Factor
Taller runners naturally have theoretically longer potential strides, but they also have more mass to move. Relative Stride Length (Stride Length / Height) is often a better efficiency indicator than absolute distance.
Factors Affecting Stride Length
1️⃣ Ground Contact Time (GCT)
The time your foot spends on the ground. Shorter GCT is associated with higher power output and better running economy.
Drill: Plyometric jumps, A-Skips, bounds.
2️⃣ Hip Extension & Power
Pushing backward through the hip at the end of the stance phase. Full extension translates to more forward propulsion.
Drill: Hill repeats, glute activation exercises, lunges.
3️⃣ Vertical Oscillation
Energy wasted moving up and down instead of forward. Excessive bounce reduces the distance traveled per calorie spent.
Drill: Run with a "low ceiling" focus, core stability work.
4️⃣ Leg Stiffness
How well your tendons and muscles act as a spring. Higher stiffness allows for more energy return with each step.
Drill: Rope skipping, pogo hops.
5️⃣ Arm Drive
The arms balance the rotation of the hips and help generate drive. Poor arm mechanics can reduce stride power.
Drill: Seated arm running, relaxed shoulder focus.
The Cadence (SPM) × Stride Length Balance
Elite runners don't just have high Cadence or high Stride Length—they have the optimal combination for their event.
Real-World Example: Eliud Kipchoge (Marathon WR)
Performance Metrics:
- Cadence (SPM): ~185 steps/min
- Stride Length: ~1.90 meters
- Velocity: ~5.85 m/s (2:52 min/km pace)
Analysis: Kipchoge maintains an exceptionally high stride length for over two hours. His efficiency comes from the ability to stay at 185 SPM while covering almost 2 meters with every full stride cycle (left + right steps).
Scenario Analysis
🔴 Overstriding (Low Cadence)
Example: 2.2m stride × 150 SPM = 2.75 m/s
Problem: Landing far in front of the center of mass creates braking forces and increases injury risk. Inefficient despite the long stride.
🔴 "Choppy" Stride (Low Stride Length)
Example: 1.1m stride × 190 SPM = 1.7 m/s
Problem: High energy cost with low propulsion. Feels busy but lacks ground coverage. Hard to sustain for long distances.
🟢 Optimized Stride (Balanced)
Example: 1.6m stride × 175 SPM = 2.3 m/s
Problem: The sweet spot where mechanical efficiency meets cardiovascular sustainability.
✅ Finding Your Optimal Balance
Set: 5 × 1km @ Threshold pace
- Rep #1: Run naturally, record your baseline Cadence and Stride Length
- Rep #2: Increase Cadence by 5 SPM (shorter, quicker steps), try to maintain pace
- Rep #3: Focus on powerful hip extension (longer stride), try to maintain pace
- Rep #4: Return to baseline cadence, focus on "springy" steps
- Rep #5: Lock in on the rhythm that felt most efficient (lowest RPE)
The repetition that felt easiest at target pace represents your current optimal balance.
Stride Index: The Power-Efficiency Metric
Formula
Stride Index combines speed and efficiency into one metric. Higher SI generally indicates superior performance potential.
Example:
Runner A: 5.0 m/s velocity × 1.6 m Stride Length = SI of 8.0
Runner B: 5.0 m/s velocity × 1.8 m Stride Length = SI of 9.0
Analysis: Runner B covers more ground per stride at the same speed, indicating better mechanical efficiency.
🔬 Research Foundation
Studies found that **increasing cadence by 10%** significantly reduces the load on the knee and hip joints, helping to prevent common injuries like runner's knee. While elite runners average 180+ SPM, focus on finding the rhythm that allows you to land your foot under your hips (neutral strike) rather than chasing a fixed number.
The key is **efficiency**: maximizing power output while minimizing the mechanical cost of movement.
Practical Training Applications
🎯 Cadence Control Set
1000m Intervals
Use a metronome or music BPM
- 1km: Baseline cadence (run naturally)
- 1km: Cadence +5 SPM (short, quick steps)
- 1km: Return to baseline cadence
- 1km: Cadence +10 SPM (focus on turnover)
Goal: Develop the neurological ability to change turnover at various speeds.
🎯 Stride Length Power Set
Hill Repeats (6-8 × 200m)
Focus on powerful hip extension
- Drive your knees forward and high
- Push forcefully off the ground
- Maintain a tall posture
Goal: Build the explosive power necessary to lengthen your stride without overstriding.
Master the Mechanics, Master the Speed
Velocity = Cadence × Stride Length isn't just a formula—it's a framework for understanding and improving every aspect of your running technique.
Track both variables. Experiment with the balance. Find your optimal combination. Speed will follow.