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Lens Equation Calculator (Thin Lens)

Solve 1/f = 1/u + 1/v for the image distance, focal length or object distance, with magnification, image height, real-vs-virtual verdict and a live three-ray diagram.

Related tools

All Physics tools →
Bernoulli equation calculatorBernoulli's principle for an ideal fluid: pressure + kinetic + potential head stays constant along a streamline, P + ½ρv² + ρgh = constant. Give the conditions at two points and leave one unknown — pressure, velocity or elevation — and it solves for it, revealing how a pipe that narrows speeds the flow and drops the pressure.Chemical Equation BalancerBalance any chemical equation instantly by solving the element matrix exactly — even tricky redox reactions.Angular Velocity CalculatorConvert RPM, rad/s, Hz and period, or derive ω from a linear speed and radius — with tangential speed and centripetal acceleration.Coulomb's Law CalculatorSolve F = kq₁q₂/εᵣr² for the force, either charge or the distance, in any of 18 dielectric media, with charges in C, µC, nC or elementary charges, plus the potential energy and the field at q₂.de Broglie Wavelength CalculatorCompute λ = h/p for an electron, proton, neutron, alpha particle, C₆₀ or any mass, from a velocity or a kinetic energy, using the relativistic momentum p = γmv.Decibel (dB) CalculatorConvert power and voltage ratios to decibels and back, and switch between dBm, dBW, watts and milliwatts.Doppler Effect CalculatorWork out the perceived frequency for a moving source or observer, classically f' = f(v ± v_o)/(v ∓ v_s) with real sound speeds, or relativistically for light — supersonic sources flagged.E = mc² Calculator (Mass–Energy)Convert mass into energy and back with a realistic efficiency — 100 % for antimatter, 0.7 % for fusion, 0.09 % for fission — and read the result in joules, kWh, kcal and tonnes of TNT.

Lens Equation Calculator (Thin Lens) works straight from this page — free, instant, nothing to install. You will find it under Physics, with Bernoulli equation calculator and Chemical Equation Balancer for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Lens Equation Calculator (Thin Lens) do?

Solve 1/f = 1/u + 1/v for the image distance, focal length or object distance, with magnification, image height, real-vs-virtual verdict and a live three-ray diagram.

When would I actually use this?

Checking a homework answer, sizing something before building it, and getting an order of magnitude before committing to a design — a torque on a bolt, the force a spring returns, the frequency a circuit resonates at, how long light takes to arrive.

What is the most common mistake?

Feeding in a value in the wrong unit. Physics formulas assume SI throughout, so grams instead of kilograms or centimetres instead of metres shifts the answer by powers of ten without any warning.

How is Lens Equation Calculator (Thin Lens) different from Bernoulli equation calculator?

They sit next to each other but answer different questions: Bernoulli equation calculator is the one to open when you need it to bernoulli's principle for an ideal fluid: pressure + kinetic + potential head stays constant along a streamline, P + ½ρv² + ρgh = constant. Give the conditions at two points and leave one unknown — pressure, velocity or elevation — and it solves for it, revealing how a pipe that narrows speeds the flow and drops the pressure. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Chemical Equation Balancer is the closest one after this: Balance any chemical equation instantly by solving the element matrix exactly — even tricky redox reactions.

What else is worth having open alongside it?

Angular Velocity Calculator and Coulomb's Law Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Constants are the CODATA values and the formulas are the textbook ones. Most assume an idealised case — no air resistance, no friction, a point mass — and the tool says so where the simplification matters.

Further reading

All guides →
ExplainerHow the Doppler Effect Works: The Formula, the Sign Convention, and Why Moving the Source Is Not the Same as Moving the ListenerFor sound, f' = f(v + v_o)/(v − v_s) — and getting the signs backwards is the classic error. Here is the convention spelled out, a 440 Hz source computed at four speeds, and why light needs a different equation entirely.ExplainerWhat Is the Reynolds Number? The Formula, the Units That Cancel, and Why 2 300 Is Only for PipesRe = ρvL/μ compares inertia with viscosity, and the units really do cancel. See the number worked out for honey, a household pipe, an artery, a swimmer and a wing — and why the 2 300 threshold belongs to pipe flow alone.ExplainerHooke's Law Explained: F = kx, Real Spring Constants, and Where It Stops HoldingHooke's law says force is proportional to stretch — but only below the elastic limit. Here is F = kx with worked numbers, what a 200 N/m spring actually feels like, and how springs combine.ExplainerHow Buoyancy Works: Archimedes' Principle, and Why Ice Floats With 10.5 % Above WaterThe upward force equals the weight of the fluid pushed aside. That one sentence decides whether something floats, and if it floats, exactly how much of it stays under.GuideThe Four Kinematics Equations: Which One to Use, and What Each One Leaves OutFive variables, four equations, and each equation is missing exactly one of them. Choose by looking at the variable the question never mentions.ExplainerProjectile Motion Explained: Range, Height, Flight Time — and Why 45° Is Not Always BestThree formulas cover the whole of projectile motion on level ground. The catch is level ground: the moment launch and landing heights differ, the 45° result stops being true.