The complete flight trajectory control manual — from your first straight shot to advanced artillery arcs.
Formula Arena is a free 2D multiplayer shooting game where mathematics is your weapon. Instead
of aiming with a mouse or joystick, you write a mathematical function f(x) that defines the exact
flight path of your bullet. Up to 8 pilots (real players and AI bots) battle in a coordinate-based arena filled
with walls and obstacles.
The game is round-based: every round you have 45 seconds to study the battlefield, write your formula, choose a firing direction, and lock it in. When the timer ends, all ships fire simultaneously and the bullets trace their mathematical curves across the arena. Last pilot standing wins the match.
Because every shot is a real mathematical function, Formula Arena doubles as a fun way to build intuition for graphs: you will quickly learn what a sine wave, a parabola, or a steep linear slope actually looks like in motion.
▶ PLAY NOW — FREEYour bullet always spawns at your ship's current position. From there, its path is controlled by your function:
x — the horizontal distance the bullet has flown so far (from 0 up to 1200 pixels).f(x) — the vertical deviation from your starting altitude at that distance.Think of your ship as the origin of a private coordinate system. Writing f(x) = 0 means "stay at
my altitude forever" — a flat, straight shot. Writing f(x) = x means "for every pixel forward, rise
one pixel" — a 45° climb.
Next to the formula input you'll find the direction toggle ▶ / ◀. It mirrors your function
horizontally, so the same formula can attack enemies on your left or your right. Always double-check the arrow
before locking in — a perfect formula fired the wrong way is a wasted round!
f(x) = 0
The bullet flies in a perfectly straight horizontal line. Ideal when an enemy sits at exactly your altitude with no walls in between.
f(x) = 0.5 * x
Climbs 1 pixel for every 2 pixels travelled. Change the coefficient to change the angle:
2 * x is steep, 0.1 * x is nearly flat, and a negative coefficient like
-0.5 * x dives downward.
f(x) = 80 * sin(x / 60)
Travels in a sine wave 80 pixels tall with a cycle length of about 60 pixels. Waves can slip through horizontal gaps between walls that straight shots can't reach.
f(x) = x - x^2 / 400
Arcs high into the sky and drops down behind tall obstacles — the classic artillery shot
for enemies hiding behind cover. Tune the 400: a smaller number makes a shorter, sharper arc; a
larger number stretches the arc further.
f(x) = 0.3 * x + 40 * sin(x / 50)
Functions can be added together! This shot climbs steadily while wobbling in a wave — hard to predict and great for confusing opponents behind partial cover.
| Category | Available |
|---|---|
| Math functions | sin(x), cos(x), tan(x), abs(x),
sqrt(x), log(x), min(a,b), max(a,b),
floor(x), ceil(x) |
| Operators | +, -, *, /, ^ (exponent),
% (modulo) |
| Constants | pi (≈ 3.1416), e (≈ 2.718) |
Syntax rule: multiplication must be written explicitly with *. Write
2 * x, never 2x. A formula with a syntax error causes your bullet to fail and detonate
instantly at your own position — embarrassing and dangerous.
A * sin(x / B), raising A makes the
wave taller; raising B makes it longer and lazier. Small B values create tight,
fast wiggles.sin(, ^ and friends instantly — every second of the 45 counts.Every match earns EXP based on your placement and eliminations. Leveling up raises your Pilot Rank, displayed next to your callsign in every lobby. Registered pilots also appear in the Global Hall of Fame leaderboard, ranked by total wins and kills.
Cosmetic items — projectile trails, impact effects and weapon skins — are purely visual. Formula Arena is never pay-to-win: a level 1 pilot with a sharp understanding of parabolas can eliminate a level 50 veteran.
Ready to test your math in combat?
▶ ENTER THE ARENAYes — the game is completely free to play in your browser, on desktop and mobile. No download or installation is required.
No. You can win plenty of matches with simple straight and sloped shots. The math depth is there when you want it — and most players find their function intuition improves naturally just by playing.
Yes. Use CREATE ROOM in the main menu to get a 5-character room code, and have friends enter it in the JOIN box. Empty slots are filled with AI bots when the match starts.
The bullet fails to launch and detonates at your position. Always check the dashed preview line — if it doesn't appear, your syntax is invalid.