Drag to turn, scroll or pinch to zoom. Tap a result to see it on the model.
3D drawing is not available on this device. Every number, formula and the calculator still work.
Know a measurement? Type it in and the lab finds the size that gives it. The other sizes stay as they are.
The same engine answers on a free API, no key needed. API docs
Two parallel bases a and c, two equal legs b. Put a second copy upside down next to it and you get a parallelogram with base a + c and height h, so the trapezoid is half of it: A = (a + c)h/2. The midline m is the average of the bases.
Given: bottom base a a = 8 cm, top base c c = 4 cm, height h = 3 cm.
Use A = ((a + c) h)/2. For example, with a = 8 cm, c = 4 cm and h = 3 cm, A = 18 cm².
Use P = a + c + 2b. For example, with a = 8 cm, c = 4 cm and h = 3 cm, P = 19.2111 cm.
Yes. In Solve, choose the area under “I know”, type its value and choose the bottom base a under “Find”. The other sizes stay as they are. For example, with c = 4 cm and h = 3 cm and A = 45 cm², a = 26 cm.
Each one has its own model, sizes you can change and the formula behind every number. Pick one to open it in the lab.
Drag a slider or type an exact value. The model, every result and every worked formula update at once, and the grid under the model counts one unit per square.
Tap a result and the model shows it: water fills a volume, paint sweeps a surface or an area, a dot walks the perimeter, vertices and edges are counted one by one.
Know the area and need the radius? Solve finds the size that gives the value you typed, then shows every other measurement for it.
Every formula is written once and evaluated by the same engine in this page and on the API, with a test that checks both give the same numbers.
Yes. Open Solve, choose the measurement you know, type its value and pick the size to find. The lab searches for the size that gives exactly that value and shows every other measurement for it, for example a circle with an area of 200 cm² has a radius of 7.9788 cm and a circumference of 50.1326 cm.
Every formula is exact and computed in double precision, then rounded to the number of decimals you choose. Two values have no exact elementary formula and are labelled as approximations: the perimeter of an ellipse (Ramanujan) and the surface of an ellipsoid (Knud Thomsen, within 1.07 %).
Millimetres, centimetres, decimetres, metres, kilometres, inches, feet and yards. Areas and volumes follow the length unit (cm², cm³), and every volume is also given in litres.
Yes. The same engine answers at https://techtools.cz/geometry-lab-api/ without a key: list the shapes, compute any of them, solve backwards, or evaluate an expression. The documentation is at https://techtools.cz/geometry-lab-api/docs.
Public JSON, no key, no sign-in. Every response carries the formula, the worked step and the value.
curl 'https://techtools.cz/geometry-lab-api/compute?shape=cone&r=3&h=4&unit=cm' curl 'https://techtools.cz/geometry-lab-api/solve?shape=circle&given=A&value=200&unknown=r' curl 'https://techtools.cz/geometry-lab-api/calc?expr=2pi*r^2&vars%5Br%5D=3' curl 'https://techtools.cz/geometry-lab-api/shapes'