Arrow Trajectory Calculator

Distance Scenario Cards — Drop & Drift Reference

The grid below deconstructs arrow trajectory by distance, one card per range. Each card shows the drop, wind drift, apex, and flight time for a 300 fps / 450-grain reference build in a 10 mph crosswind — the same math the simulator above runs for custom inputs. Click a card or use the filter to highlight the distance you are tuning for.

Notice how drop scales faster than distance — 20 to 40 yards roughly quadruples the drop (7.7 → 31 inches), because drop grows with the square of time of flight. This is why your sight pin gaps widen dramatically past 40 yards, and why a 10 fps speed change moves your 50-yard pin by several inches while barely moving your 20-yard pin.

The Physics of Arrow Drop — Parabolic Trajectory

An arrow drop calculator answers one physical question: how far does gravity pull the arrow down during its flight? The arrow leaves the bow horizontally (relative to your sight line), and gravity acts on it the entire time it is airborne. The longer the flight, the more time gravity has to act — and drop grows with the square of that time.

Drop Formula d = ½gt²

The drop formula is pure Newtonian physics: d = ½gt², where g = 32.174 ft/s² (Earth's gravity) and t is the time of flight in seconds. Time of flight comes from horizontal distance ÷ arrow speed: t = distance / speed. At 40 yards (120 ft) with a 300 fps arrow, t = 120 / 300 = 0.4 s, and drop = 0.5 × 32.174 × 0.4² × 12 = 30.9 inches.

The critical insight is the square on t. Doubling the distance more than doubles the drop — 20 to 40 yards (2× distance) gives 4× the drop, because t doubles and t² quadruples. This is the single most important fact for sight-pin spacing, and it is why long-range archery demands precise speed knowledge: a 5% speed error becomes a 10% drop error at distance.

Apex Height & Flight Time

When you aim slightly up to compensate for drop (which is what a sight pin does), the arrow traces a parabola that peaks above your line of sight at the trajectory midpoint. That apex height is approximately drop ÷ 4 — so a 300 fps arrow at 40 yards (31-inch drop) peaks about 7.7 inches above your line of sight at the 20-yard midpoint. This matters for clearing branches: a high-apex trajectory needs midrange clearance, not just target clearance. Flight time (t) is the same number that drives drop, and it also sets how long a crosswind has to push the arrow sideways.

Air Drag & Wind Drift

An arrow ballistics calculator or archery ballistics calculator adds two forces the pure parabolic model ignores: air drag (which slows the arrow over distance, increasing real drop slightly) and crosswind (which pushes it sideways). Drag matters most at long range and high speed; crosswind matters whenever there is wind.

Drag Force F = ½ρv²CdA

The drag force on an arrow follows F = ½ρv²CdA, where ρ is air density (~0.002377 slugs/ft³ at sea level), v is velocity, Cd is the arrow's drag coefficient (~0.2–0.4 for a fletched arrow), and A is frontal area. Over a 40-yard flight this drag bleeds roughly 5–10% of the arrow's speed, which increases the real drop by 2–5% versus the pure parabolic model. For pin-sight tuning at bowhunting distances the parabolic approximation is close enough; for 80+ yard target or crossbow shots the drag-decay correction becomes worth applying.

Crosswind Drift Calculation

Crosswind drift is drift = wind_speed × time_of_flight × drag_factor. The wind pushes the arrow for the entire flight time, and the drag factor (~0.55 for a 350-grain arrow, scaled inversely by weight) captures how much the wind actually grips the fletching and shaft. A heavier arrow drifts less because it has more inertia to resist the lateral force — a 595-grain arrow in a 10 mph crosswind drifts about 30% less than a 350-grain arrow at the same speed and distance. This is one reason heavy hunting arrows are more forgiving in wind, beyond their penetration advantage.

Sight-Pin Compensation Table (20–70 yd)

The reference table below shows drop and drift at each pin distance for a 300 fps / 450-grain build. Use the drop column to set pin gaps: each pin sits lower in the sight housing than the one above it by the drop difference between those distances. Re-set pins whenever your speed changes by more than 5 fps.

Arrow Speed Drop & KE at Distance — How Deceleration Eats Your Energy

The Speed @ Dist and KE @ Dist columns above answer the arrow energy at yardage question: how fast is the arrow still traveling — and how much energy does it still carry — when it finally reaches 40 or 60 yards? The drop model on this page is parabolic (gravity only), so the two new columns use a separate simplified drag-decay model: v(d) = v₀ × e^(−k·d), with k ≈ 0.0013 per yard for a typical 5/16″ carbon hunting arrow with vanes (Cd ~0.4). For the 300 fps reference build that means ~285 fps at 40 yards and ~277 fps at 60 yards — roughly 5–8% of muzzle speed gone before the arrow ever touches the target.

The KE numbers fall roughly twice as fast (in percentage terms) as the speed numbers, because kinetic energy scales with the square of velocity: the 450-grain reference build starts at 89.9 ft-lbs at the muzzle, holds ~81 ft-lbs at 40 yards, and ~77 ft-lbs at 60 yards — a 10–14% energy tax from air drag alone. That asymmetry is the whole reason hunters check their ethical game-class floor at maximum yardage, not at the muzzle: a build that clears 65 ft-lbs standing at the bow can slide under the large-game floor at 60 yards. Run your own downrange speed through the Arrow Kinetic Energy Calculator to check the floor at the distance you actually shoot, and remember heavier arrows both start with more KE and bleed speed slower (a smaller k), which compounds their downrange energy advantage.

Bow Type Trajectory Comparison

Compound, recurve, and crossbow trajectories differ primarily because of speed. A faster bow gives the arrow less flight time at any given distance, which means less drop and a flatter pin gap — but also less time for a crosswind to act, so less drift. The comparison below uses typical speeds for each bow class at 40 yards.

Your trajectory build card — copy to your notes

# Arrow trajectory build card
arrow_speed     = 300 fps
arrow_weight    = 450 gr
distance        = 40 yd
crosswind       = 10 mph
---
flight_time     = 0.4000 s
drop            = 30.89 in
wind_drift      = 2.51 in
apex_height     = 7.72 in
pin_angle       = 1.229 deg

Frequently Asked Questions

From Trajectory Numbers to a Tuned Sight

The simulator above returns drop, drift, apex, and flight time for your exact build — but trajectory is downstream of speed, which is downstream of your bow and arrow. If you do not yet know your real arrow speed, run the homepage arrow speed calculator first with your IBO rating and real draw parameters, then bring that fps back here. A 10 fps error in your speed input moves the 50-yard drop by 6+ inches.

Want the full formula derivation — the drag-decay model, the pin-shift field method, and the 20–60 yard worked examples? Read the companion long-form guide: How to Calculate Arrow Trajectory. For the energy your arrow delivers at impact, run the Arrow Kinetic Energy Calculator with the speed and weight you used here.