Physics & Mechanics · 14 calculators
Physics & Mechanics questions, answered
Work out speed, force, energy, motion, waves and gas behavior from the standard physics formulas. 14 questions, one per calculator, each naming its formula and figure at documented inputs. Open any one to swap in your own numbers. Every answer in Physics & Mechanics states the calculator’s formula, the worked-example inputs behind the figure, the result at those inputs and the point where the model stops being a reasonable approximation, so each number can be checked against your own situation before you rely on it. The questions in Physics & Mechanics run from the ones most people ask first to the ones that only matter once the basics are settled, and every answer links to the calculator that produced its figure, so the reasoning and the arithmetic can be read side by side and challenged separately.
Common physics & mechanics questions
Why does kinetic energy grow with the square of speed?
Energy of motion is half the mass times the speed squared, so doubling the speed quadruples it. A car at 60 mph carries four times the energy of the same car at 30, which is why stopping distances lengthen so fast.
What is the difference between mass and weight?
Mass is how much matter an object has, in kilograms. Weight is the force gravity puts on that mass, in newtons. The same mass weighs about a sixth as much on the Moon.
How does horsepower relate to torque?
Power is torque times rotational speed. Horsepower equals torque in pound-feet times RPM divided by 5,252, so at 5,252 RPM the two numbers are equal.
Is gravity the same everywhere on Earth?
Not quite. The standard value is 9.81 meters per second squared, but it runs from about 9.78 at the equator to about 9.83 at the poles, and it falls slightly with altitude. For everyday work 9.81 is plenty.
Do these physics calculators include air resistance?
No. They use the textbook formulas, which assume no air resistance and no friction. A real object falls or flies less far than the result, and a light object with a large surface is affected most.
What is the difference between speed and velocity?
Speed is how fast something moves. Velocity is speed with a direction. A car circling a track at a steady 30 mph has a constant speed and a changing velocity, because its direction keeps changing.
Which units do the formulas expect?
Meters, kilograms and seconds, which give newtons, joules and watts. A speed in miles per hour or a mass in pounds needs converting first, or the result will be wrong by a fixed factor.
Is the ideal gas law accurate for real gases?
It works well for gases at moderate pressure and well above their condensing temperature. Near condensation or at high pressure, real gases depart from it, and a more detailed model is needed.
Why does a projectile launched at 45 degrees go farthest?
On level ground with no air resistance, the range is greatest at 45 degrees, because that angle balances the time in the air against the forward speed. Angles equally far above and below 45 give the same range.
Physics & Mechanics at a glance: each result, and the input that moves it most
| Calculator | Result at the worked example | Input that moves it most |
|---|---|---|
| Horsepower Calculator | Horsepower: 285.6 | Torque (lb-ft) (57.1 (20%)) |
| Speed, Distance and Time Calculator | Average speed per hour: 48 | Hours (45.7 (95%)) |
| Kinetic Energy Calculator | Kinetic energy (joules): 468,750 | Speed (m/s) (191,250 (41%)) |
| Newton's Second Law Force Calculator | Force (newtons): 686.7 | Acceleration (m/s²) (140 (20%)) |
| Uniform Acceleration Calculator | Final speed (m/s): 25 | Acceleration (m/s²) (4 (16%)) |
| Hooke's Law Calculator | Spring force (N): 30 | Spring constant (N/m) (6 (20%)) |
| Ideal Gas Law Calculator | Pressure (atm): 1 | Volume (L) (0.207 (21%)) |
| Gravitational Potential Energy Calculator | Potential energy (J): 490.5 | Mass (kg) (98.1 (20%)) |
| Work and Power Calculator | Work done (J): 519.6 | Force (N) (103.9 (20%)) |
| Wavelength and Frequency Calculator | Wavelength (m): 3 | Frequency (MHz) (0.606 (20%)) |
| Projectile Motion Calculator | Range (m): 40.8 | Launch speed (m/s) (16.3 (40%)) |
| Free Fall Calculator | Fall time (s): 3.2 | Gravity (m/s²) (0.318 (10.0%)) |
| Centripetal Force Calculator | Centripetal force (N): 9,600 | Speed (m/s) (3,840 (40%)) |
| Pendulum Period Calculator | Period (s): 2 | Pendulum length (m) (0.201 (10%)) |
How to calculate each physics & mechanics figure
How do I calculate horsepower?
Horsepower = torque (lb-ft) × RPM ÷ 5,252; kilowatts = horsepower × 0.7457. Compare an engine's output at a given RPM with the figure quoted on its spec sheet. Using the worked example on the page, the horsepower works out to 285.6.
How do I calculate speed, distance and time?
Speed = distance ÷ time; time in hours = hours + minutes ÷ 60. Check whether a trip's average speed fits the schedule you planned. At the worked-example inputs the average speed per hour is 48.
How do I calculate kinetic energy?
KE = ½ × mass × speed²; momentum = mass × speed. See how much more energy a small increase in speed adds. Using the worked example on the page, the kinetic energy (joules) works out to 468,750.
How do I calculate newton's second law force?
Force = mass × acceleration (Newton's second law); 1 lbf = 4.448222 N. Convert a mass and an acceleration into the force a rope, bolt or motor must carry. At the worked-example inputs the force (newtons) is 686.7.
How do I calculate uniform acceleration?
v = u + a × t; s = u × t + ½ × a × t²; average speed = s ÷ t. Predict how far and how fast something goes when it speeds up at a steady rate. The prefilled example returns a final speed (m/s) of 25.
How do I calculate hooke's law?
Force = k × x; stored elastic energy = ½ × k × x². Check the load a spring carries or the energy it stores at a given stretch. Run it at the prefilled values and the spring force (n) comes out at 30.
How do I calculate ideal gas law?
P = n × R × T ÷ V, with R = 0.082057 L·atm ÷ (mol·K). Estimate the pressure in a sealed container as the temperature or volume changes. Run it at the prefilled values and the pressure (atm) comes out at 1.
How do I calculate gravitational potential energy?
Gravitational potential energy = m × g × h. See how much energy a lifted load stores and releases if it falls. At the worked-example inputs the potential energy (j) is 490.5.
How do I calculate work and power?
Work = F × d × cos θ; power = work ÷ time; 1 horsepower = 745.7 W. Find the energy a push or a pull transfers, and how fast it happens. At the worked-example inputs the work done (j) is 519.6.
How do I calculate wavelength and frequency?
Wavelength = speed of light ÷ frequency; period = 1 ÷ frequency; c = 299,792,458 m/s. Turn a radio station or a Wi-Fi channel's frequency into the size of its wave. Run it at the prefilled values and the wavelength (m) comes out at 3.
How do I calculate projectile motion?
Range = v² × sin 2θ ÷ g; maximum height = v² × sin² θ ÷ (2g); flight time = 2v × sin θ ÷ g, on level ground with no air resistance. Predict where a thrown or launched object lands on level ground. Run it at the prefilled values and the range (m) comes out at 40.8.
How do I calculate free fall?
Fall time = √(2h ÷ g); impact speed = √(2 × g × h), ignoring air resistance. Estimate how long a drop takes and how fast the object hits, ignoring air. Using the worked example on the page, the fall time (s) works out to 3.2.
How do I calculate centripetal force?
Centripetal acceleration = v² ÷ r; force = m × v² ÷ r. Check the grip a vehicle needs to hold a turn at a given speed. The prefilled example returns a centripetal force (n) of 9,600.
How do I calculate pendulum period?
Period = 2π × √(L ÷ g), for small swings; frequency = 1 ÷ period. Find the swing time of a pendulum, a swing or a clock weight. Using the worked example on the page, the period (s) works out to 2.
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