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🏗️ Engineering & constructionFree
Rotational Power Calculator
A shaft carrying 120 N·m at 25 rad/s transmits 3000 W. Multiply torque by angular velocity measured at the same operating point to check motors, gearboxes and…
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🏗️ Engineering & constructionFree
Angular to arc distance calculator
A wheel with a 0.35 m radius that turns one full revolution, 2π radians, rolls 2π × 0.35 m, its whole circumference: the calculator multiplies the radius by the…
K
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🏗️ Engineering & constructionFree
Gravitational field strength calculator
Earth's mass of 5.972 × 10²⁴ kg at 6,371,000 m from its centre gives a field of 9.81997342622 m/s²: enter any mass and distance to get the pull a test object…
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🏗️ Engineering & constructionFree
Hollow sphere moment of inertia
A thin spherical shell of 3 kg and radius 2 m has a moment of inertia of 8 kg·m² about any diameter, from I = (2/3) mr².
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🏗️ Engineering & constructionFree
Rolling shapes race calculator
On a 30° ramp, a solid sphere beats a solid cylinder, which beats a thin hoop: the smaller the inertia factor, the faster a shape rolls.
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🏗️ Engineering & constructionFree
Torque Wrench Force Calculator
Reaching 120 N·m with a wrench 0.5 m long takes 240 N at the handle. Enter the target torque and the effective length to get the pull, and see why a longer…
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🏗️ Engineering & constructionFree
Escape energy calculator
Enter Earth's 5.972 × 10²⁴ kg and a launch radius of 6,371,000 m, add your object's mass, and you get the ideal minimum energy to leave the planet for good.
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🏗️ Engineering & constructionFree
Gravitational potential calculator
At 6,371,000 m from the centre of a 5.972 × 10²⁴ kg mass, the size of the Earth, the gravitational potential is −62,563,050.6985 J/kg.
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🏗️ Engineering & constructionFree
Orbit altitude from period calculator
Pick the orbital period you need and get the height above the surface that delivers it: for a 90-minute Earth orbit, enter 5400 seconds with the planet's size…
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🏗️ Engineering & constructionFree
Synchronous orbit radius calculator
For Earth, with a mass of 5.9722e24 kg and a sidereal day of 86164.0905 s, a synchronous orbit sits 42164.2437691 km from the centre.
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🏗️ Engineering & constructionFree
Vis-viva calculator
With μ of 398600.4418 km³/s², a distance of 7000 km and a semi-major axis of 10000 km, the orbital speed is 8.60382451787 km/s.
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➗ MathFree
Compare fractions
Find out which of two fractions is larger, exactly: 3/4 beats 2/3, and 1/2 and 2/4 come out equal because they are the same value.
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➗ MathFree
Complementary angle calculator
Find the angle that completes an acute angle to a right angle, so the complement of 30° is 60° and that of 12.5° is 77.5°.
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🏗️ Engineering & constructionFree
Mutual gravitational acceleration calculator
Two bodies feel the same gravitational pull, but the lighter one accelerates more: enter the Earth, the Moon and 384,400,000 m between their centres to see each…
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🏗️ Engineering & constructionFree
SHM maximum acceleration calculator
An oscillation with a 0.15 m amplitude at 4 rad/s reaches a peak acceleration of 2.4 m/s². Enter amplitude and angular frequency to get the largest acceleration…
K
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🏗️ Engineering & constructionFree
Mass-spring period calculator
Hang 2 kg on a spring of 50 N/m and find how long one complete bounce takes, in seconds. Enter the mass and the spring constant to get the period of an ideal…
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🏗️ Engineering & constructionFree
SHM velocity calculator
With an amplitude of 5 m and an angular frequency of 2 rad/s, an oscillator 3 m from equilibrium moves at 8 m/s.
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➗ MathFree
Compatible numbers
Estimate a quotient or product the way you would in your head: 417 ÷ 6.1 becomes 420 ÷ 6 = 70, shown next to the exact 68.36, so you can tell at a glance…
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➗ MathFree
Completing the square
Rewrite ax² + bx + c in vertex form and read the parabola at a glance: 2x² − 8x + 5 becomes 2(x − 2)² − 3, with its vertex at (2, −3).
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🏗️ Engineering & constructionFree
Second-class lever calculator
A wheelbarrow carrying 200 N at 0.4 m from the wheel, lifted at handles 1.2 m from it, needs 66.6666666667 N of effort, a mechanical advantage of 3.
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🏗️ Engineering & constructionFree
Pendulum bob maximum speed calculator from length and angle
Release a 2 m pendulum at 30 degrees from the vertical and get the speed of the bob at the bottom of its swing, plus how far it drops on the way.
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🏗️ Engineering & constructionFree
Oscillator quality factor calculator
A resonance at 1200 Hz with a 30 Hz half-power bandwidth has a quality factor of 40. Enter both values in the same unit and get Q, the single figure that tells…
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🏗️ Engineering & constructionFree
Springs in parallel calculator
Three parallel springs of 120, 180 and 300 N/m act like a single spring of 600 N/m. List each stiffness and get the combined value and the number of springs…
K
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➗ MathFree
Completing the square with worked steps
See every step that turns ax² + bx + c into vertex form: x² + 6x + 2 becomes (x + 3)² − 7, with the vertex at (−3, −7), by halving 6 to 3 and adding and…
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➗ MathFree
Complex number calculator
Do arithmetic on two complex numbers a + bi in one place: (3 + 2i) times (1 − 4i) gives 11 − 10i. Division uses the exact conjugate formula and refuses a zero…
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➗ MathFree
Complex number to polar form
Describe a complex number by distance and direction instead of coordinates: 3 + 4i sits at magnitude 5, and 2i points straight up at 90°, with the angle also…
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➗ MathFree
Complex number to rectangular form
Turn a modulus and an argument back into a + bi: a modulus of 2 at 60 degrees gives a real part of 1 and an imaginary part of about 1.732.
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➗ MathFree
Complex number to trigonometric form
Rewrite a + bi as r(cos θ + i sin θ), ready to copy: 1 + i has modulus √2 and argument 45°, also given in radians.
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🏗️ Engineering & constructionFree
Archimedes principle calculator
Water at 1000 kg/m³ displaced by 0.002 m³ under 9.81 m/s² pushes up with 19.62 N: the calculator multiplies density, volume and gravity following Archimedes'…
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🏗️ Engineering & constructionFree
Simply supported beam center load calculator
A 1000 N load at the middle of a 6 m beam puts 500 N on each support and a maximum bending moment of 1500 N·m under the load.
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🏗️ Engineering & constructionFree
Will It Float Calculator
An object of 750 kg/m³ in water of 1000 kg/m³ floats, with a density ratio of 0.75: compare any object with any fluid and get a clear verdict, the signed…
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🏗️ Engineering & constructionFree
Gear train mechanical advantage calculator
Two stages of 20 to 60 and 15 to 45 teeth give a 9:1 ideal torque ratio, with the output turning the same way as the input: enter each mesh in order and see…
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🏗️ Engineering & constructionFree
Gravitational force comparison
Masses of 10 and 20 at a distance of 2 pull 16 times harder than masses of 5 and 10 at a distance of 4: enter two setups and see which attracts more strongly…
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🏗️ Engineering & constructionFree
Hydraulic lift calculator
Pistons of 2 and 10 cm turn a 100 N push into 2,500 N, because the force grows with the square of the diameter ratio.
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🏗️ Engineering & constructionFree
Manometer pressure calculator
A water column difference of 0.25 m under 9.81 m/s² means a pressure difference of 2452.5 Pa between the two ports.
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🏗️ Engineering & constructionFree
Pendulum energy calculator
Pick any point of the swing and see where the energy sits: a 0.5 kg bob on a 1 m string released at 30 degrees already carries most of it as motion by 15…
S
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🏗️ Engineering & constructionFree
Projectile time at height calculator
A ball launched at 20 m/s and 60° passes 10 m twice, once on the way up and once on the way down; this calculator gives both moments and the highest point it…
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🏗️ Engineering & constructionFree
Tipping angle stability
An object with a 0.4 m base and its centre of gravity 0.8 m high tips over at 14.0362434679°. Enter the base width and the centre of gravity height to see how…
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Runs in your browser
🏗️ Engineering & constructionFree
Torsional pendulum period
A body with a moment of inertia of 0.05 kg·m² on a wire of 0.2 N·m/rad swings with a period of 3.14159265359 s.
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🏗️ Engineering & constructionFree
Two-member bracket force calculator
With a 1000 N load and members at 30° and 120°, the first carries 500 N and the second 866.025404 N, both in tension.
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➗ MathFree
Lucas theorem calculator
Get C(n, k) modulo a prime without huge factorials: C(1000, 200) modulo 7 is 1, found by writing both numbers in base 7 and multiplying small digit binomials.
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➗ MathFree
Modular nth root calculator
Find every k-th root of a number modulo a prime: the square roots of 2 modulo 17 are 6 and 11, listed in order.
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➗ MathFree
Multiplicative order calculator
Find the smallest power that brings a number back to 1 modulo n: powers of 2 modulo 9 run 2, 4, 8, 7, 5, 1, so the order is 6.
K
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➗ MathFree
Baby-step giant-step calculator for discrete logarithms
2 raised to the 9th power leaves a remainder of 5 when divided by 13, so the discrete logarithm of 5 to base 2 modulo 13 is 9.
K
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➗ MathFree
Count primitive roots modulo n
Modulo 18 there are exactly 2 primitive roots, the value of Euler's totient applied twice. Enter a modulus and see how many generators it has, or a clear notice…
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➗ MathFree
Complex root calculator
Get every nth root of a complex number, not only the principal one: the cube roots of −8 are −2 and 1 ± √3 i, all of magnitude 2, at 60°, 180° and 300°.
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➗ MathFree
Condition number calculator
See how much a matrix can magnify small errors in your data: rows (2, 1) and (1, 2) give a condition number of 3, the largest singular value divided by the…
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➗ MathFree
Cone surface area calculator
Get every area of a right circular cone from its radius and slant height: radius 3 and slant height 5 give a lateral area of 15π and a total of 24π, base…
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➗ MathFree
Idempotents modulo n calculator
Modulo 12 there are four residues that stay the same when squared: 0, 1, 4 and 9. Enter any modulus up to one trillion to get the complete sorted list, plus the…
B
Runs in your browser
➗ MathFree
Deterministic Miller–Rabin test
97 is prime: it passes all seven fixed bases, 2, 3, 5, 7, 11, 13 and 23, proven to settle every whole number up to 9007199254740991.
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➗ MathFree
Nth power residue checker
Tells you whether a number is a k-th power modulo a prime: 2 is a square modulo 7, because 2 raised to the power 3 leaves remainder 1.
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➗ MathFree
Quadratic non-residues list mod p
Lists every remainder that is never a square modulo an odd prime: modulo 7 the squares are 1, 2 and 4, so the non-residues are 3, 5 and 6.
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➗ MathFree
Solovay-Strassen primality test with a chosen base
For 13 with base 2, both residues come out as 12, so 13 passes and is a probable prime to base 2. A mismatch would prove the number composite, with the base as…
K
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➗ MathFree
Conic section classifier
Enter the six coefficients of a general second-degree equation and see which curve it draws: x² + y² − 25 = 0 is a circle centered at (0, 0), with discriminant…
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➗ MathFree
Fermat pseudoprime checker for any base
Find out if a composite number passes Fermat’s test anyway: 341 with base 2 leaves residue 1, so it is a Fermat pseudoprime to base 2.
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Runs in your browser
➗ MathFree
Lucas pseudoprime checker
Spot the odd composites that fool the Lucas test: with P equal to 1 and Q equal to −1, the composite 323 still passes, making it the smallest Fibonacci…
A
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➗ MathFree
Prime signature calculator
Shows the shape of a number's prime factorization without the primes: 360 = 2³ × 3² × 5 has signature [3, 2, 1].
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➗ MathFree
Proth primality test
Proves a Proth number k × 2^n + 1 prime with a single witness; taking k as 3 and n as 2 gives 13, and witness 2 raised to 6 leaves 12, that is −1 modulo 13, so…
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➗ MathFree
Smallest prime factor calculator
Finds the least prime that divides your number, plus what is left after dividing: for 84 the smallest prime factor is 2 and the cofactor is 42.
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➗ MathFree
Complex conjugate calculator
Enter the real and imaginary parts and get the conjugate: 3 + 2i becomes 3 − 2i. It is the step behind dividing complex numbers and finding a modulus squared…
H
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