// multi-utility computation suite · offline · instant · precise
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sci.projectile-range-angle Calculator
Calculates horizontal range of a projectile launched at angle θ with initial velocity v₀ from an elevated platform height h above the landing surface. Non-zero launch height shifts the optimal angle below 45° — numerical optimisation finds the exact angle for maximum range.
Inputs
V0 M S
Rate of movement. 1 m/s = 3.6 km/h = 2.237 mph.
Theta Deg
Reference formula or conversion factor shown for context.
H0 M
Vertical measurement. For health calculators, typically standing height without shoes.
G M S2
Rate of velocity change (m/s²). Earth's gravity: 9.81 m/s². Objects in free fall accelerate at this rate.
Results
horizontal range R (m)
The difference between the maximum and minimum values.
maximum height H (m)
The largest value in the dataset or feasible range.
time of flight t (s)
The computed duration or time value.
R = v₀²sin(2θ)/g (flat ground)
The value at the specified point or condition.
optimal angle for max range
The difference between the maximum and minimum values.