动能计算器
This kinetic energy calculator uses the formula KE = ½mv² to solve for kinetic energy (joules), mass (kg), or velocity (m/s). Choose what you want to find, enter the two known values, and get an instant result with energy unit conversions.
Kinetic Energy Calculator
Use the formula KE = ½mv² to solve for kinetic energy, mass, or velocity. Select what you want to find, enter the two known values, and get instant results.
常见问题
如何计算动能？
动能公式为 KE = ½mv²，其中 m 是物体质量（kg），v 是速度（m/s），计算结果单位为焦耳（J）。速度对动能的影响是平方关系，速度加倍则动能变为原来的 4 倍。
动能和势能有什么关系？
根据机械能守恒定律，在无摩擦的理想情况下，动能和重力势能可以相互转换，总量保持不变。例如，自由落体时势能（mgh）转化为动能（½mv²），最终落地速度可由此计算。
什么是相对论性动能？
当物体速度接近光速时，经典力学的动能公式不再适用，需使用相对论动能公式：KE = (γ-1)mc²，其中 γ = 1/√(1-v²/c²) 是洛伦兹因子，c 是光速。在日常速度范围内，两公式结果几乎相同。
为什么车辆碰撞速度越快危害越大？
由于动能与速度的平方成正比，速度增加一倍时动能增加四倍。例如，车辆以 60 mph 行驶时的动能是 30 mph 时的 4 倍，碰撞力也相应增大 4 倍，这就是为什么速度对交通安全至关重要。
Understanding Kinetic Energy
The KE Formula (½mv²)
Kinetic energy is the energy an object possesses because of its motion. Any object with mass that is moving at a velocity greater than zero has kinetic energy. The standard SI formula is:
Kinetic Energy Formula:
KE = ½ × m × v²
- KE = Kinetic energy (Joules, J)
- m = Mass (kilograms, kg)
- v = Velocity (metres per second, m/s)
The formula can be rearranged to solve for any of its three variables:
Solve for mass:
m = 2KE / v²
Solve for velocity:
v = √(2KE / m)
Kinetic energy is always non-negative because mass is always positive and velocity is squared. Doubling the mass doubles the kinetic energy, but doubling the velocity quadruples it — this quadratic relationship explains why high-speed collisions are disproportionately more destructive than low-speed ones.
Derivation from the Work-Energy Theorem
The kinetic energy formula is derived from Newton's second law and the definition of work. When a net force F is applied over a displacement d, the work done on an object is:
W = F × d
F = m × a (Newton's second law)
v² = u² + 2ad → d = (v² − u²) / 2a
W = m × a × (v² − u²) / 2a = ½m(v² − u²)
Starting from rest (u = 0): W = ½mv²
The work done on an object from rest equals the kinetic energy acquired. This is the work-energy theorem: the net work done on an object equals the change in its kinetic energy.
Real-World Examples
Baseball Pitch
A regulation baseball has a mass of about 0.145 kg. A fastball leaves the pitcher's hand at around 42 m/s (≈ 94 mph). What is its kinetic energy?
KE = ½ × 0.145 × 42² = ½ × 0.145 × 1764 ≈ 127.9 J
About 128 joules — comparable to a 60-watt light bulb running for roughly 2 seconds.
Family Car on the Motorway
A 1,500 kg car travelling at 30 m/s (108 km/h, about 67 mph) has kinetic energy of:
KE = ½ × 1500 × 30² = ½ × 1500 × 900 = 675,000 J = 675 kJ
675 kilojoules — enough to boil roughly 1.6 litres of water from room temperature. This illustrates why braking distances grow so rapidly with speed.
Rifle Bullet
A 9 mm bullet typically has a mass of about 0.008 kg (8 g) and leaves the barrel at approximately 370 m/s:
KE = ½ × 0.008 × 370² = ½ × 0.008 × 136900 ≈ 547.6 J
Over 500 joules from just 8 grams, almost entirely due to its high velocity — showing why speed has a far greater effect on kinetic energy than mass.
Cyclist at Speed
A 70 kg cyclist riding at 10 m/s (36 km/h):
KE = ½ × 70 × 10² = ½ × 70 × 100 = 3,500 J = 3.5 kJ
3.5 kJ, which all needs to be dissipated by brakes or ground friction when stopping.
Energy Unit Conversions
The SI unit for energy is the joule (J). Here are common conversion factors to help you interpret kinetic energy results in practical contexts:
| Unit | Symbol | Equivalent in Joules |
|---|---|---|
| Joule (SI base unit) | J | 1 J |
| Kilojoule | kJ | 1,000 J |
| Megajoule | MJ | 1,000,000 J |
| Calorie (thermochemical) | cal | 4.184 J |
| Kilocalorie (food Calorie) | kcal | 4,184 J |
| Watt-hour | Wh | 3,600 J |
| Kilowatt-hour | kWh | 3,600,000 J |
| British Thermal Unit | BTU | 1,055.06 J |
| Foot-pound | ft·lb | 1.35582 J |
| Electronvolt | eV | 1.60218 × 10⁻¹⁹ J |
To convert from joules: divide by the "Equivalent in Joules" value. For example, 675,000 J ÷ 3,600 = 187.5 Wh = 0.1875 kWh.