Work & Energy Calculator

Work Formula:

W = F × d × cos(θ)
Where: W = Work, F = Force, d = Distance, θ = Angle between force and displacement

Force (F) - Newtons:

Distance (d) - meters:

Angle (θ) - degrees:

Work (W) - Joules:

Common Angles:
0° = Same direction (cos 0° = 1)
90° = Perpendicular (cos 90° = 0)
180° = Opposite direction (cos 180° = -1)

Kinetic Energy Formula:

KE = ½mv²
Where: KE = Kinetic Energy, m = Mass, v = Velocity

Mass (m) - kg:

Velocity (v) - m/s:

Kinetic Energy (KE) - Joules:

Initial Velocity (v₁) - m/s:

Final Velocity (v₂) - m/s:

Work-Energy Theorem:
W = ΔKE = KE₂ - KE₁

Gravitational Potential Energy:

PE = mgh
Where: PE = Potential Energy, m = Mass, g = Gravity (9.81 m/s²), h = Height

Mass (m) - kg:

Height (h) - meters:

Gravity (g) - m/s²:

Potential Energy (PE) - Joules:

Standard Gravity: g = 9.81 m/s²
Moon Gravity: g ≈ 1.62 m/s²
Mars Gravity: g ≈ 3.71 m/s²

Conservation of Mechanical Energy:

E_total = KE + PE = Constant
KE₁ + PE₁ = KE₂ + PE₂ (no friction)
½mv₁² + mgh₁ = ½mv₂² + mgh₂

Mass (m) - kg:

Initial Velocity (v₁) - m/s:

Initial Height (h₁) - m:

Final Velocity (v₂) - m/s:

Final Height (h₂) - m:

Energy Lost to Friction (J):