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Projectile Motion Calculator

Science & Engineering

Range, max height and flight time at any angle

Quick Answer

Projectile Motion Calculator: Range, max height and flight time at any angle. vx = v·cosθ (constant); vy = v·sinθ − gt.

Presets:

Range

40.8 m

Flight 2.88 s · Max height 10.2 m

Flight time2.88 s
Max height10.19 m
Landing speed20.00 m/s
Range40.77 m

Velocity split at launch (v=20 m/s)

vx (horizontal)14m/s (50.0%)vy (vertical)14m/s (50.0%)

Solution steps (no air drag)

  1. 1vx = v·cosθ = 20×cos45° = 14.14 m/s；vy = v·sinθ = 20×sin45° = 14.14 m/s
  2. 2Flight time from h(t)=0: t = (vy + √(vy² + 2g·h₀))/g = 2.883 s
  3. 3R = vx × t = 14.14 × 2.883 = 40.77 m
  4. 4H = h₀ + vy²/(2g) = 0 + 14.14²/19.62 = 10.19 m

Range by angle (same speed)

AngleRangeMax heightTime
15°20.4 m1.4 m1.06 s
30°35.3 m5.1 m2.04 s
37°39.2 m7.4 m2.45 s
45° ★ ←40.8 m10.2 m2.88 s
53°39.2 m13.0 m3.26 s
60°35.3 m15.3 m3.53 s
75°20.4 m19.0 m3.94 s

💡 On flat ground (h₀=0), 45° gives maximum range; from a height the optimal angle drops slightly below 45°. Real projectiles face air drag — golf balls lose ~30% range vs vacuum.

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How to Use

  1. Enter known quantities: fill values and confirm units in the Projectile Motion Calculator.
  2. Instant solution: unknowns solve live with the formula shown transparently.
  3. Use constant/material tables: standard physical constants and material data are listed on this page.
  4. Compare conditions: change inputs to compare scenarios.

Key Points

  • Projectile Motion Calculator is a free online science & engineering tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Range, max height and flight time at any angle.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Projectile motion (no air resistance)

vx = v·cosθ (constant); vy = v·sinθ − gt
Flight time: T = 2v·sinθ / g
Max height: H = (v·sinθ)² / 2g
Range: R = v²·sin(2θ) / g — maximal at θ = 45°
g = 9.8 m/s²

Example: v=20 m/s, θ=45° → T ≈ 2.89 s, H ≈ 10.2 m, R ≈ 40.8 m.

FAQ

How do I use the Projectile Motion Calculator?
Open the page and fill in the input fields — results update automatically. Range, max height and flight time at any angle.
Are the results accurate?
Yes. Standard formulas and conversion factors are used and verified.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. Everything runs locally in your browser.

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Source & Updates

Based on CODATA recommended constants and standard physics formulas. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Projectile Motion Calculator[EB/OL]. https://www.yijiansuan.com/en/c/science/projectile

Results provided by this tool are for reference only and do not constitute professional advice.