What this physics formula calculator does
This tool bundles 15 of the most common physics formulas taught in Pakistani class 9, 10 and F.Sc courses into a single calculator. Pick a formula from the dropdown, and the input panel rebuilds itself to show only the variables that formula needs — labelled with their symbols, names and SI units. Enter the values you know, press Calculate, and the tool returns the result with unit, step-by-step substitution, and a short interpretation. Every formula is solved for its standard subject: enter u, a, t and get v; enter m, a and get F; enter V, I and get R. The tool catches the domain errors that matter — zero time, zero mass, zero area, zero resistance — and explains why each is not physically meaningful.
Formula reference
All 15 formulas use SI units throughout. Refer to this table if you want to check the exact form or the units of any variable.
| Formula | Meaning | Units |
|---|---|---|
| v = u + at | First equation of motion | m/s = m/s + m/s² × s |
| s = ut + ½at² | Second equation of motion | m = m/s × s + m/s² × s² |
| v² = u² + 2as | Third equation of motion | m²/s² = m²/s² + m/s² × m |
| F = ma | Newton's second law | N = kg × m/s² |
| W = mg | Weight (g = 9.8 m/s²) | N = kg × m/s² |
| W = Fd | Work (force along displacement) | J = N × m |
| W = Fd cos θ | Work at angle θ | J = N × m × (dimensionless) |
| KE = ½mv² | Kinetic energy | J = kg × m²/s² |
| PE = mgh | Gravitational potential energy | J = kg × m/s² × m |
| P = W / t | Power (rate of work) | W = J / s |
| ρ = m / V | Density | kg/m³ = kg / m³ |
| P = F / A | Pressure | Pa = N / m² |
| V = IR | Ohm's law | V = A × Ω |
| s = d / t | Speed | m/s = m / s |
| p = mv | Linear momentum | kg·m/s = kg × m/s |
Worked examples
Example 1: v = u + at (a car accelerating)
- v = 0 + 3 × 8 = 24 m/s.
- A car starting from rest with a 3 m/s² acceleration reaches 24 m/s after 8 seconds.
Example 2: F = ma (a pushed box)
- F = 12 × 4 = 48 N.
- Newton's second law: 48 newtons of net force are needed.
Example 3: KE = ½mv² (a moving cricket ball)
- KE = ½ × 0.15 × 30² = 0.5 × 0.15 × 900 = 67.5 J.
- Note the velocity is squared — doubling v quadruples KE. This is why fast-moving objects carry disproportionate energy.
Example 4: ρ = m / V (finding the density of a metal block)
- ρ = 0.54 / 0.0002 = 2700 kg/m³.
- This value is close to the density of aluminium (2700 kg/m³), so the block is likely aluminium.
Example 5: V = IR (Ohm's law)
- V = 0.5 × 12 = 6 V.
- A current of 0.5 amperes through a 12-ohm resistor requires a potential difference of 6 volts.
Example 6: s = ut + ½at² (finding displacement)
- ut = 5 × 6 = 30 m.
- ½at² = 0.5 × 2 × 6² = 0.5 × 2 × 36 = 36 m.
- s = 30 + 36 = 66 m.
- The two terms show the contribution of the initial velocity (30 m) and the acceleration (36 m).
Notes on units and constants
- All formulas use SI units. Convert centimetres to metres, grams to kilograms, and minutes to seconds before entering values.
- Gravitational acceleration (g) — the tool uses 9.8 m/s² for the weight formula. Some textbooks use 10 m/s² for convenience. Use 9.8 for accurate work and 10 for rough estimates.
- Angle θ in W = Fd cos θ must be in degrees. The tool converts to radians internally and returns cos θ in the step-by-step.
- Density and pressure involve volumes and areas which are often given in cm³ and cm². Convert to m³ and m² first: 1 m² = 10,000 cm², 1 m³ = 1,000,000 cm³.
- Velocity is a vector — its direction matters. This tool computes magnitudes and assumes all motion is along a single line unless angle is an input.
Common mistakes to avoid
- Mixing units. Distance in metres but time in minutes, or mass in grams but volume in m³ — these are the most frequent errors. Convert everything to SI before entering.
- Forgetting to square the velocity in KE. KE = ½mv², not ½mv. A common slip in exams.
- Using weight instead of mass in F = ma. Weight is already a force (W = mg, in newtons). F = ma takes mass in kilograms.
- Treating g as 10 everywhere. Fine for rough estimates, but for exam answers use the value your textbook specifies.
- Wrong angle in W = Fd cos θ. The angle is between the force vector and the displacement vector, not between the force and the horizontal (unless the object moves horizontally).
- Resistance of zero in Ohm's law. That would imply infinite current, which is a domain error. Real circuits always have some resistance.
- Ignoring direction in the equations of motion. If the object decelerates, use a negative value of a. The tool accepts negative numbers for velocity and acceleration.
FAQ
Which physics formulas are included?
The tool includes 15 formulas: three equations of motion (v = u + at, s = ut + ½at², v² = u² + 2as), force (F = ma), weight (W = mg), work (W = Fd cos θ), kinetic energy (KE = ½mv²), potential energy (PE = mgh), power (P = W/t), density (ρ = m/V), pressure (P = F/A), Ohm's law (V = IR), speed (s = d/t), and momentum (p = mv).
What is the SI unit system used?
All formulas use SI units. Length in metres (m), mass in kilograms (kg), time in seconds (s), force in newtons (N), energy in joules (J), power in watts (W), density in kg/m³, pressure in pascals (Pa), voltage in volts (V), current in amperes (A), and resistance in ohms (Ω).
How do I calculate acceleration from velocity and time?
Use a = (v − u) / t, where v is final velocity, u is initial velocity, and t is time. This is the rearranged form of the first equation of motion, v = u + at. Select 'v = u + at' from the dropdown and enter the three known values.
What is the difference between work and power?
Work is the energy transferred when a force moves an object over a distance, measured in joules (J). Power is the rate at which work is done, measured in watts (W), where 1 W = 1 J/s. A 100 J task done in 2 s uses 50 W of power.
Why does the tool reject a time value of 0?
Time of zero would make acceleration, speed, or power undefined because the formulas all divide by time. A physics problem with zero elapsed time is not physically meaningful — it is a domain error.
Does this replace a scientific calculator?
No. This tool evaluates each formula step by step with unit awareness and clear input labels, which makes it useful for homework checks and quick estimates. For anything involving trigonometric values, roots, or algebraic manipulation, use the scientific calculator tool.
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Revise the theory behind these formulas with our Class 9 notes and Class 10 notes, and track term progress with the free Student Portal.