Physics Equation Calculator: Solve Any Formula

This physics equation calculator solves for any variable in common physics formulas. You enter the known values, select the formula, and it returns the unknown quantity with the correct units. It covers kinematics, Newton’s laws, energy, work, power, and more.

Formula

The calculator uses the standard textbook equations from classical mechanics. Each formula is written with the variables defined below.

• Kinematics (constant acceleration): v = v₀ + at and d = v₀t + ½at²
• Newton’s second law: F = ma
• Work: W = Fd (when force and displacement are in the same direction)
• Kinetic energy: KE = ½mv²
• Gravitational potential energy: PE = mgh

Variables: v₀ = initial velocity (m/s), v = final velocity (m/s), a = acceleration (m/s²), t = time (s), d = displacement (m), F = force (N), m = mass (kg), W = work (J), KE = kinetic energy (J), PE = potential energy (J), g = acceleration due to gravity (9.81 m/s²), h = height (m).

Worked Example

Using the default values (Kinematics v=v₀+at, v₀=0 m/s, a=2 m/s², t=5 s):

1. Write the equation: v = v₀ + at
2. Substitute values: v = 0 + (2)(5)
3. Multiply: v = 0 + 10
4. Result: v = 10 m/s

The calculator shows 10.00 m/s as the final velocity.

How to Use the Calculator

Select the formula you need from the dropdown. Then enter the known values in the input fields. The calculator computes the result automatically as you type. For example, to find force with F=ma, enter mass and acceleration; the result appears in newtons.

Each formula has specific required inputs. If you leave a field at zero, the calculator uses that zero as the value. For most formulas, zero is a valid input, but for kinetic energy or potential energy, a zero mass or velocity gives a zero result, which is correct.

Common Mistakes and Unit Issues

The most frequent error is mixing units. Always convert to SI units before entering values: meters for distance, seconds for time, kilograms for mass. If you have kilometers per hour, divide by 3.6 to get m/s. If you have grams, divide by 1000 to get kg.

Another mistake is using the wrong formula for the situation. The kinematics equation v = v₀ + at only works for constant acceleration. If acceleration changes, you need calculus or numerical methods. Similarly, W = Fd only applies when force is constant and parallel to displacement. For force at an angle, use W = Fd cosθ.

Rounding errors can accumulate in multi-step problems. Keep intermediate values with full precision and round only the final answer. The calculator rounds to two decimal places, but you may need more for precise work.

Limitations of These Formulas

These equations are from classical mechanics, valid for everyday speeds and sizes. They break down near the speed of light, where relativistic effects matter, or at atomic scales, where quantum mechanics applies. For objects moving at significant fractions of light speed, use relativistic formulas. For particles like electrons, quantum mechanics is required.

Air resistance is ignored in these basic formulas. In real-world scenarios like falling objects or projectile motion, air drag can change results noticeably. The formulas assume a vacuum or negligible friction.

How to Choose the Right Formula

Identify what you know and what you need to find. List the known quantities and the unknown. Then match them to the formulas:

• If you have initial velocity, acceleration, and time, and need final velocity, use v = v₀ + at.
• If you have force and mass, and need acceleration, use a = F/m.
• If you have mass and velocity, and need kinetic energy, use KE = ½mv².
• If you have mass, height, and gravity, and need potential energy, use PE = mgh.

When multiple formulas could apply, check which one has all but one variable known. That unknown is what you solve for.

Frequently Asked Questions

Can this calculator solve for any variable in the formula?

Yes, you can rearrange the formula manually to solve for any variable. For example, if you have force and mass and need acceleration, enter force as the mass field and mass as the acceleration field? No, that’s wrong. Instead, use the formula F=ma and enter force and mass, then compute a = F/m. The calculator only computes the standard form, so you must rearrange algebraically yourself.

What if my units are not in meters and seconds?

Convert to SI units first. For example, if distance is in kilometers, multiply by 1000 to get meters. If time is in minutes, multiply by 60 to get seconds. The calculator assumes all inputs are in the units shown next to each field.

Does this work for projectile motion?

Partially. The kinematics formulas work for the vertical and horizontal components separately, but you must break the motion into components. The calculator does not handle vectors directly. For a projectile launched at an angle, you would use the initial velocity components and apply the formulas to each axis.

Is the acceleration due to gravity always 9.81 m/s²?

No, 9.81 m/s² is the standard average at Earth’s surface. It varies slightly with altitude and latitude. For most physics problems, 9.81 m/s² is accurate enough. On the Moon it’s about 1.62 m/s², and on Mars about 3.71 m/s².

Why do I get a negative result?

A negative result indicates direction. In kinematics, negative velocity means motion in the opposite direction to the chosen positive axis. Negative work means the force opposes the displacement. Negative potential energy can occur if you set the reference point above the object.

Can I use this for rotational motion?

No, these are linear motion formulas. For rotation, you need analogous equations with angular velocity, angular acceleration, torque, and moment of inertia. The units are different (radians, rad/s, N·m).

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sel formula | Formula | Kinematics v=v0+at=1, Kinematics d=v0t+.5at^2=2, Newton F=ma=3, Work W=Fd=4, Kinetic Energy KE=.5mv^2=5, Potential Energy PE=mgh=6
in v0 | Initial velocity | m/s | 0 | 0
in v | Final velocity | m/s | 10 | 0
in a | Acceleration | m/s² | 2 | 0
in t | Time | s | 5 | 0
out result | Result | - | (formula==1 ? v0+a*t : formula==2 ? v0*t+0.5*a*t*t : formula==3 ? v0*a : formula==4 ? v0*a : formula==5 ? 0.5*v0*v*v : v0*v*a) | 2