High Jump Approach Calculator
J-approach curve radius from athlete speed and height.
About this calculator
This calculator works backward from the height you want to clear to the physics needed to clear it, modeling the modern Fosbury Flop technique rather than an old-style straddle or scissors jump. It starts by estimating your standing center of mass at 55% of body height, then adds the extra rise needed to get that center of mass up to the bar height — plus a conservative arch-margin buffer (assumed 10 cm) on top, since this model treats the back-arch as adding required clearance rather than letting it subtract from it, effectively asking the center of mass to rise slightly higher than the bar itself so the calculated approach speed leaves room to spare. From that required rise, it applies v = √(2 × g × Δh) to find the minimum vertical takeoff velocity, then combines it with a takeoff angle (modeled as decreasing slightly for higher bar heights, since taller clearances favor more horizontal speed over pure vertical lift) to get the full takeoff velocity vector, and finally divides by a conversion efficiency (assumed 88%, since not all approach speed converts cleanly into takeoff velocity) to find the required approach speed.
The distinctive J-curve — the final curved steps of a Fosbury approach — is modeled with centripetal-force physics: radius = v² / (g × tan(lean angle)), where the inward lean increases with approach speed. Treat every output as a physics-based estimate of an idealized technique, not a coaching prescription — real jumpers vary lean angle, curve length, and technique efficiency well outside these fixed assumptions, and this model doesn't account for individual leg strength, jumping technique flaws, or bar-clearance style beyond the generic Fosbury arch.
Inputs
Results
Required Approach Speed
6.94 m/s
How to Use This Calculator
- Enter Target bar height, Athlete height, and Athlete mass.
- Set Approach steps and Average stride length.
- Review the Required Approach Speed (m/s) result.
- Use J-Curve Radius (m) and Lean Angle in Curve (°) to inform your decision.
How the result changes with Target bar height
| Target bar height | Required Approach Speed |
|---|---|
| 1 | 2.06 m/s |
| 1.42 | 4.74 m/s |
| 2.6 | 9.99 m/s |
What each input means
- Target bar height
- Bar height you want to clear.
- Athlete height
- Athlete's standing height.
- Athlete mass
- Body mass in kilograms.
- Approach steps
- Total number of steps in approach run (typically 8-12).
- Average stride length
- Average stride length during approach.
What each result means
- Required Approach Speed
- Approach speed needed to clear the bar.
- J-Curve Radius
- Radius of the curved portion of the approach.
- Lean Angle in Curve
- Inward lean angle during curved approach.
- Takeoff Speed
- Speed at the moment of takeoff.
- Vertical Velocity
- Vertical component of takeoff velocity.
- Horizontal Velocity
- Horizontal component of takeoff velocity.
- Takeoff Angle
- Angle of takeoff from horizontal.
- Total Approach Distance
- Full approach run length including straight and curve.
- Curve Distance
- Length of the curved J-portion of the approach.
- Flight Time
- Time the athlete is airborne.
- COM Rise Required
- How much the centre of mass must rise above standing height.
- Takeoff Kinetic Energy
- Total kinetic energy at takeoff.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersTarget bar height = 1.9, Athlete height = 1.8, Athlete mass = 75, Approach steps = 10 = 5 input(s) provided
- Calculate Required Approach SpeedRequired Approach Speed = totalTakeoffSpeed / conversionEfficiency6.94 = 6.94
- Calculate J-Curve Radius16.18 = 16.18
- Calculate Lean Angle in CurveLean Angle in Curve = max(12, min(30, leanAngleDeg))16.9 = 16.9
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does the arch-margin assumption seem to make the required approach speed higher rather than lower?
In a real Fosbury flop, the arch lets the athlete's centre of mass pass below the bar, which could let a jumper clear a given height with slightly less vertical velocity than raw physics implies. This model instead treats the 10 cm arch margin as extra required rise added on top of the bar height, a deliberately conservative choice, so the calculated approach speed leaves a safety margin rather than being cut to the bare minimum.
Why does the takeoff angle get smaller as the target bar height increases?
The model computes takeoff angle as 50° minus 8° for every metre above 1.5 m of target height, clamped between 38° and 55°, reflecting that clearing higher bars typically favors more horizontal approach speed relative to vertical lift. At the same total takeoff speed, a lower angle shifts more of that speed into the horizontal component, which the required-vertical-velocity relationship then demands be compensated for elsewhere.
What is the J-Curve Radius output actually measuring?
It's the radius of the curved final steps of your approach, from radius = approach speed² ÷ (g × tan(lean angle)), where the lean angle itself increases with your calculated approach speed. A faster approach speed produces both a larger lean angle and, through this formula, a wider curve radius — faster jumpers need a more gradual curve into the bar rather than a tight one.
Should I train to hit the exact numbers this calculator gives me?
No — treat every output as a physics-based estimate for a generic, idealized Fosbury technique, not a personalized coaching target. The model relies on fixed assumptions (88% approach-to-takeoff conversion efficiency, a 10 cm arch margin, a standing centre of mass at 55% of height) that don't reflect your individual leg strength or technique, so use it to understand how speed, height, and body proportions interact rather than as a number to chase in training.
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