Why does 45° give the longest range?

Range depends on sin(2θ), which peaks when 2θ = 90°. This holds on flat ground without air resistance.

How do I convert watt-hours to joules?

Multiply by 3,600, because a watt is one joule per second and an hour has 3,600 seconds.

Is thrust horsepower the same as engine horsepower?

No. Thrust horsepower is the useful power delivered. Engine horsepower is higher because propellers and drivetrains are not 100% efficient.

Does the projectile calculator include air resistance?

No. It models ideal motion, so real objects travel less far, especially light or fast ones.

Physics Calculators

Physics calculators for motion and energy: model projectile trajectories, convert electrical energy between joules and watt-hours, and turn thrust into horsepower.

Projectile Motion Calculator

Calculate the trajectory, max height, range, and flight time of a projectile.

kinematics physics trajectory

Volts to Joules Calculator

Convert voltage to electrical energy in Joules using charge (V × Q) or current and time (V × I × t).

electricity energy voltage

Watt Hour Calculator

Calculate energy in watt-hours (Wh) and kilowatt-hours (kWh) from power and time, or from voltage, current and time.

electricity energy watt hours

Thrust to Horsepower Calculator

Convert thrust in pounds or Newtons into thrust horsepower using speed, with optional propeller efficiency.

aviation thrust horsepower

Motion: projectile trajectories

Projectile motion splits a launch into two independent parts: constant horizontal velocity and vertical motion under gravity. The Projectile Motion Calculator works out flight time, maximum height, and range from launch speed, angle, and starting height, and plots the path.

It models ideal motion with no air resistance, which is accurate for dense, slow objects over short distances and increasingly optimistic for light or fast ones. Without drag, the maximum range from flat ground occurs at a 45° launch angle.

Electrical energy and power

Energy is power multiplied by time. The Watt Hour Calculator converts a device’s wattage and running time into watt-hours and kilowatt-hours, the unit your electricity bill and battery capacities use. The Volts to Joules Calculator finds energy from voltage and charge, or from voltage, current, and time.

Thrust and horsepower

Thrust is a force, and force only does work when something moves. The Thrust to Horsepower Calculator converts thrust and speed into thrust horsepower for aircraft, boats, and drones, with an optional propeller efficiency to estimate the engine power required. At zero speed, thrust horsepower is zero.

Key formulas

Horizontal range (flat ground): R = v₀² × sin(2θ) ÷ g
Electrical energy: E (J) = V × Q = V × I × t
Energy in watt-hours: Wh = W × hours; kWh = Wh ÷ 1,000
Thrust horsepower: HP = thrust (lbf) × speed (mph) ÷ 375

Getting accurate results

Keep units consistent: the projectile calculator uses g = 9.80665 m/s² unless you change it.
Battery capacity in mAh must be multiplied by voltage to get watt-hours.
Use real cruise thrust for horsepower; static thrust ratings overstate power at speed.
Remember 1 Wh = 3,600 J when comparing results between calculators.

Frequently asked questions

Why does 45° give the longest range?: Range depends on sin(2θ), which peaks when 2θ = 90°. This holds on flat ground without air resistance.
How do I convert watt-hours to joules?: Multiply by 3,600, because a watt is one joule per second and an hour has 3,600 seconds.
Is thrust horsepower the same as engine horsepower?: No. Thrust horsepower is the useful power delivered. Engine horsepower is higher because propellers and drivetrains are not 100% efficient.
Does the projectile calculator include air resistance?: No. It models ideal motion, so real objects travel less far, especially light or fast ones.

Browse other categories:

Finance → Health → All Calculators →