Engineering Calc Tools

Calculus

Equation Solver with Units

Solve one equation or a system for any unknowns, with known values in any units and answers in the units you choose.

Tool no.
ECT-G01
Rev
1.0
Updated
Oct 2026
Method
Newton’s method with unit conversion
Examples

Given

Knowns: m = 5 kg, p = 200 kPa, theta = 30 deg, T = 25 degC. Equations use the names only: F = m*a, p*V = n*R*T. Ask for a unit with F in kN; give a starting guess with x ~ 2. Functions: sqrt, sin, cos, tan, asin, exp, log (natural), log10, abs; constants pi and e.

Answers

Unknown = —
Runs in your browser. Nothing you enter is uploaded.Newton’s method with SI unit conversion
How to use this solver

Write each equation exactly as it appears in your notes, using a name for every quantity. Then give the known values on their own lines with their units, in any mix of SI and US units. Whatever is left over is solved for; you need as many equations as unknowns. This is the tool for problems no dedicated calculator covers: energy balances, kinematics with several unknowns, Bragg’s law, gas mixtures, and so on.

How it works

Unitsevery known is converted to SI base units (kg, m, s, K, A, mol), so the equations are always consistent
Newton’s methodxn+1 = xn − J−1f(xn), started from several guesses
One unknownthe equation is scanned from −10⁶ to 10⁶ and every sign change becomes a root

Worked example

A 5 kg block drops 0.4 m onto a 2000 N/m spring: how far does the spring compress? (the default)

  1. Energy: ½kd² = mg(h + d), so 1000d² − 49.05d − 19.62 = 0.
  2. The quadratic has two roots, d = 0.1667 m and d = −0.1177 m; only the positive one is physical.
  3. d = 16.67 cm.

Frequently asked questions

Why is “m = 5 kg” a known but “F = m*a” an equation?

A line whose right side is a number, with or without a unit, gives a value. Any other line is an equation to satisfy. So write a constant with a unit as its own line (g = 9.81 m/s^2) rather than inside an equation.

What about temperatures?

Temperatures in degC or degF are converted to kelvin, which is right for gas laws and for differences. For a temperature change on its own, write it in K (a change of 20 °C is 20 K).