How do you rearrange a formula to make a variable the subject?

To make a variable the subject: (1) Identify where the target variable appears, (2) Use inverse operations to undo each operation on the variable, (3) Apply the same operation to both sides. For example, to make t the subject of v = u + at: subtract u from both sides to get v - u = at, then divide by a to get t = (v - u) / a.

How do you rearrange formulas with squares?

If the variable is squared, isolate the squared term first, then take the square root. For E = mc^2, to solve for c: divide both sides by m to get c^2 = E/m, then c = sqrt(E/m).

How do you rearrange when the variable is in the denominator?

Multiply both sides by the denominator to remove the fraction. For s = d/t, to solve for t: multiply both sides by t to get st = d, then divide by s to get t = d/s.

What if the variable appears more than once?

Collect all terms containing the variable on one side, factor the variable out, then divide. For example, if ax + b = cx + d, subtract cx from both sides: (a-c)x + b = d, subtract b: (a-c)x = d - b, divide: x = (d-b)/(a-c).

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Rearrange a Formula

Enter formula (e.g. v = u + at, F = ma, E = mc^2)

Solve for variable

How It Works

What is rearranging?

Rearranging a formula means rewriting it so a different variable is alone on one side. For example, rearranging v = u + at for t gives t = (v - u) / a.

Inverse operations

To isolate a variable, undo operations in reverse order. If the variable is added, subtract. If multiplied, divide. If squared, take the square root.

Common physics formulas

v = u + at, s = ut + 0.5at^2, F = ma, E = mc^2, PV = nRT. Rearranging these for different variables is a core physics and algebra skill.

Keeping equations balanced

Whatever you do to one side, do to the other. This keeps the equation true while isolating your target variable step by step.

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