Solve for any quantity
Pick the circle beside the quantity you want and it becomes the unknown. The same beam formula gives the deflection, the load it can carry, or the stiffness it needs.
TOOL 04 / FORMULAS
Pick a formula. Solve it for anything in it.
Over 200 formulas from mechanics to chemistry. Choose the quantity you want, fill in the rest, and the answer updates as you type.
No account required · Right in your browser · Works offline once opened
SLIDE RULE / FormulasSCREENSHOT
WHAT IT DOES
A formula sheet that does the algebra.
Each formula is a small solver of its own. You never rearrange it by hand, and you never wonder which unit a symbol was in.
Answers as you type
There is no button to press. Change a value and the result follows, which makes it easy to see what a longer span or a stiffer section does.
Every symbol explained
Each quantity has its name and SI unit beside it, and many formulas have a diagram showing what each length, force and angle refers to.
Type expressions, not just numbers
A field takes 200e9 or pi*0.05^2/4 as readily as a number, so a derived input does not need a separate calculation.
Measurements with uncertainty
Enter a value as 2.31 ± 0.02 and the uncertainty is propagated through the formula to the answer.
Add your own
Write a formula of your own once and it is kept under My formulas and solved in the same way. Send any result to the calculator or a worksheet.
WHAT IS COVERED
Twelve subjects, searchable as one list.
The formulas of a first engineering degree and the physics and chemistry beside it. Search by name or by the formula itself, or browse a subject.
Every formula works in SI units. To use a value in other units, convert it in the unit converter or type it into the calculator first.
MECHANICS AND STRUCTURES
- Mechanicskinematics, dynamics, energy, rotation, gravitation
- Solid mechanicsstress, bending, torsion, deflection, buckling
- Fluid mechanicshydrostatics, flow, losses, drag
ELECTRICAL
- Electrical circuitsDC, capacitors, inductors, AC
- Electromagnetismelectrostatics, magnetism, induction
- Control & signalsfirst and second order, frequency response
THERMAL
- Thermodynamicsheat, gases, cycles
- Heat transferconduction, convection, radiation, fins, exchangers
SCIENCE AND MATHS
- Waves & optics
- Modern physics
- Chemistrysolutions, gases, acids, kinetics, electrochemistry
- Maths & geometry
A FEW OF THEM
Formulas you will recognise.
Each is in the solver under the name shown, ready to be solved for any of its symbols.
- FORMULAAS WRITTENSUBJECT
Simply supported beam, central loadδ = F·L³/(48·E·I)Solid mechanics, deflection and buckling.Euler buckling loadP = π²·E·I/(K·L)²Solid mechanics, deflection and buckling.Bending stressσ = M·y/ISolid mechanics, bending and torsion.Projectile range (level ground)R = v²·sin(2θ)/gMechanics, kinematics.Voltage dividerV_out = V_in·R₂/(R₁ + R₂)Electrical circuits, DC circuits.LC resonant frequencyf = 1/(2π·√(L·C))Electrical circuits, AC circuits.Simple pendulum periodT = 2π·√(L/g)Mechanics, rotation and oscillation.
QUESTIONS
Before you open it.
Can it rearrange a formula for me?
Yes. Choose the quantity you want to find and the solver works it out from the others, whichever side of the equals sign it was on.
What units does it use?
SI units throughout, shown beside every field: newtons, metres, pascals, kilograms. A field accepts an expression, so 200e9 is a quick way to enter 200 GPa.
Can I add a formula that is not there?
Yes. Add your own formula and it is kept with the others under My formulas. Signed in, your formulas are saved to your account.
Is it free?
Yes. Every formula is part of the free plan, with no account needed.
One of eight tools that work together.
A value from one goes straight into another- CalculatorScientific and symbolic, with the steps behind each answer.
- Unit converterEvery unit of a quantity at once, and compound units.
- ReferenceConstants, materials, steam tables and section properties.
- Graph2D curves, 3D surfaces and curve fitting to data.
- SolversMatrices and systems with working, and differential equations.
- StatisticsDistributions and hypothesis tests with confidence intervals.
- WorksheetA whole problem on one sheet, with units and live results.
- The whole toolkit →See how the eight tools fit together, and what is free.
Find the formula. Skip the rearranging.
Open the formula solver — Free ↗No account required. Free for every tool; Pro adds unlimited worksheets and exports.