Sideways at constant speed (nothing pushes it horizontally) and downward under gravity. Split the launch into v·cosθ and v·sinθ and solve each alone.
R = v² sin 2θ / g. It peaks at 45° and is symmetric: 30° and 60° land in the same spot.
h = h₀ + (v sinθ)² / 2g. A steeper launch climbs higher but travels less far.
No drag, no wind, no spin. Real projectiles, especially light or fast ones, fall short and steeper.
Horizontal and vertical motion are independent. Horizontal: constant speed v·cosθ. Vertical: starts at v·sinθ and slows, stops, then falls under gravity. Solve each separately, then combine.
On level ground, R = v²·sin(2θ)/g. It peaks at θ = 45° and is symmetric: 30° and 60° reach the same distance. Launching from a height shifts the best angle lower.
h = h₀ + (v·sinθ)²/(2g). Only the vertical component matters; a steeper launch climbs higher but travels less far.
Gravity there is about a sixth of Earth’s (1.62 against 9.81 m/s²), so the same throw goes about six times farther and stays up six times longer. Mass does not matter: without drag a cannonball and a pebble land together.
This model leaves out drag, so it overestimates range and height, sometimes a lot for light or fast objects. It is the clean physics-class ideal, useful for intuition rather than real ballistics. The golf mode on this page is the opposite case: it models drag and spin lift.
Range depends on the product of horizontal speed and hang time. Lower angles have more horizontal speed but less hang time; higher angles the reverse. 45° balances them — on level ground. Launch from a height and the best angle drops below 45°.
Not here. Without air resistance, all projectiles follow the same path regardless of mass — a cannonball and a pebble launched identically land together. Add drag and that changes.
For dense, slow, heavy objects over short distances, barely. For light objects, high speeds, or long ranges, very — real range can be a fraction of the ideal. Treat this as the frictionless ideal.
Gravity is about ⅙ of Earth's, so the same throw goes roughly six times farther and stays up about six times longer. Switch the gravity buttons to see it.
Split the launch into horizontal v·cosθ and vertical v·sinθ. At time t, x = v cosθ · t and y = h0 + v sinθ · t − ½ g t². Without air resistance the path is a parabola: at 20 m/s and 45° from the ground it flies for 2.9 s, peaks at 10.2 m and lands 40.8 m away.
| Club | Ball speed | Launch | Backspin | Carry | Total | Apex |
|---|
Gravity, drag opposing motion through the air, and Magnus lift, the force from spin that also curves a soccer free kick.
Backspin holds the ball up and extends carry. Tilt the spin axis off vertical and the same effect pulls it sideways into a draw or fade.
All three forces are integrated numerically in 3D (RK4): downrange, height and left/right curve.
Wind, altitude, lie, ball and surface, or the Moon and Mars, each alter the drag and lift acting on the ball.
Absolute numbers vary enormously between golfers; the ratios between clubs within one bag do not. Loft, shaft length and lie angle set those ratios, and they are much the same set of clubs for everyone. So if you know one club honestly, scaling the rest by the same speed factor lands close, usually within a few yards per club. What it cannot capture is a bag that is genuinely inconsistent: a driver you hit badly and a 7-iron you hit beautifully will produce an estimate that flatters one end and insults the other. Spin is scaled at reduced strength for the same reason, since spin follows loft and strike far more than speed.
The distributions here describe populations. Being at the 60th percentile of average amateurs means 60% of that group swings slower; it says nothing about your handicap, because scoring is dominated by short game and course management, not speed. Plenty of single-figure players sit mid-pack on ball speed and beat people who out-drive them by 40 yards. Treat the curve as a speed benchmark, not a ranking of golfers.
Every real spin is a mix of the two: backspin (the dominant component, creating lift) and sidespin (the smaller component that curves the ball left or right). The “spin axis” slider here controls that mix: 0° is pure backspin, and larger tilts trade some lift for curve.
Ball speed divided by clubhead speed, a measure of strike efficiency. A pure driver strike can approach 1.5; shorter, more lofted clubs sit lower (1.1–1.3) because more of the impact energy goes into spin and less into ball speed.
The lift coefficient here depends on the spin ratio: spin speed relative to ball speed, not spin rate alone. A driver’s high ball speed gives it a low spin ratio despite thousands of rpm, which is exactly why drivers are hit with far less backspin than wedges.
High loft trades ball speed for launch angle and spin: the same swing speed produces a slower, higher-spinning, steeply-climbing shot that trades distance for stopping power and control near the green.
Magnus lift fights gravity for longer, flattening the descent and extending the time the ball spends moving forward before it falls — up to a point. Too much spin (a "sky ball") adds height without adding distance, since the extra lift steepens the whole trajectory instead of extending it.
Grass gets trapped between the clubface and the ball at impact — the "flyer lie" — reducing the friction that normally imparts spin. Less backspin means less lift and a lower, longer-rolling, less controllable shot, which is exactly why rough is harder to stop on the green from.
Thinner air means less drag and less Magnus lift working on the ball — the classic "ball flies farther in Denver" effect. It also means slightly less lift, so very high-spin, high-altitude shots can fly a little flatter than expected even as they go farther overall.
Each bounce is a real, separately-integrated arc — vertical speed reflects off the surface at that surface's restitution (a lot of energy lost on sand or green, much less on hardpan), horizontal speed is cut by its friction, and the cascade repeats until the bounce height becomes genuinely negligible, followed by a decelerating roll-out. It's calibrated to realistic total distances, not a full contact-mechanics simulation — read individual bounce heights as illustrative, not laboratory measurements.
Every row recalculates under whatever conditions are currently set, using each club's own pro-average launch numbers — so the table always answers "how would each club do right now," not a fixed reference condition. If you've adjusted a club's own ball speed, launch or spin away from its pro average, the callout above the table compares your actual dialled-in shot to what a pro would get with that same club under those same conditions.
The Moon has no atmosphere at all — drag and Magnus lift both vanish entirely, wind is meaningless, and the ball follows a pure gravity-only arc at ⅙ Earth gravity (a real driver would sail for hundreds of yards). Mars keeps a thin CO₂ atmosphere — about 0.6% of Earth's sea-level pressure — so wind and altitude still matter, just far more weakly, on top of roughly ⅓ Earth's gravity.
For the Tour-average driver launch on this page (167 mph, 10.9°) the drag-free formula gives about 231 yards, while the simulated ball carries 267. Backspin gives the ball Magnus lift that outweighs the drag slowing it, so the vacuum range is a baseline, not a prediction.
Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.