Calculator™ © - Free Online Calculators

Online Calculators since 2009

- Physics Tutorials, Physics Revision and Physics Calculators
- Uniformly Accelerated Decelerated Circular Motion Calculator
- Uniform Circular Motion Calculator
- Torque Calculator
- Restoring Force In Shm Calculator
- Impulse Calculator
- Kepler Third Law Calculator
- Kinematics of Linear SHM Calculator
- Newtons Second Law For A System Of Particles Calculator
- Kinematics of Linear SHM Calculator
- Orbital Velocity Calculator

The Vector Calculator is provided in support of our Physics Tutorials on Vectors and Scalars which explores addition and subtraction of vectors, multiplication of a vector by a scalar, dot (scalar) product of two vectors and the vector product of two vectors with practical working examples and formula. A list of the supporting Vector and Scalar Physics Tutorials is available at the bottom of this page. This calculator will calculate:

- The magnitudes of each vectors when the coordinates are given
- The sum of two vectors
- The difference of two vectors
- The dot product of two vectors
- The magnitude of the cross product of two vectors
- The angle between two vectors

These results will be used to find the following physical quantities:

- The resultant of two vector quantities
- Work done by a force when it moves an object at a certain linear distance
- Moment of a force
- The angle between a Force and Linear distance a system moves linearly or rotates around a fixed point (pivot)

Magnitude of Vector u⃗ (|u⃗|) | |

Magnitude of Vector v⃗ (|v⃗|) | |

Sum of Vectors u⃗ and v⃗ (u⃗+v⃗) | |

Difference of Vectors u⃗ and v⃗ (u⃗-v⃗) | |

Dot Product of Vectors u⃗ and v⃗ (u⃗∙v⃗) | |

Magnitude of the Cross Product of Vectors u⃗ and v⃗ (|u⃗∙v⃗|) | |

Cosine of Angle Formula and Calculation (cos θ) | |

Sine of Angle Formula and Calculation (sin θ) | |

Tan of Angle Formula and Calculation (tan θ) | |

Angle θ (angle θ) |

Please note that the formula for each calculation along with detailed calculations is shown further below this page. As you enter the specific factors of each vector calcualtion, the Vector Calculator will automatically calculate the results and update the formula elements with each element of the vector calculation. You can then email or print this vector calculation as required for later use.

We hope you found the Vector Calculator useful, if you did, we kindly request that you rate this calculator and, if you have time, share to your favourite social network. This allows us to allocate future resource and keep these Physics calculators and educational material free for all to use across the globe.

|u*⃗*| = √**u**^{2}_{x} + u^{2}_{y} + u^{2}_{z}

|u*⃗*| = √^{2} + ^{2} + ^{2}

|u*⃗*| = √ + +

|u*⃗*| =

|u

|u

|u

|v*⃗*| = √**v**^{2}_{x} + v^{2}_{y} + v^{2}_{z}

|v*⃗*| = √^{2} + ^{2} + ^{2}

|v*⃗*| = √ + +

|v*⃗*| =

|v

|v

|v

u*⃗* + v*⃗* = u_{x} + u_{y}, u_{z} + v_{x}, v_{y} + v_{z}

u*⃗* + v*⃗* = + , + , +

u*⃗* + v*⃗* =

u

u

u*⃗* - v*⃗* = u_{x} - u_{y}, u_{z} - v_{x}, v_{y} - v_{z}

u*⃗* - v*⃗* = - , - , -

u*⃗* - v*⃗* =

u

u

u*⃗*∙v*⃗* = (u_{x}∙v_{x}) + (u_{y}∙v_{y}) + (u_{z}∙v_{z})

u*⃗*∙v*⃗* = (∙) + (∙) + (∙)

u*⃗*∙v*⃗* =

u

u

|u*⃗*∙v*⃗*|_{x} = u_{y} ∙ v_{z} - u_{z} ∙ v_{y}

|u*⃗*∙v*⃗*|_{x} = ∙ - ∙

|u*⃗*∙v*⃗*|_{x} =

|u

|u

|u*⃗*∙v*⃗*|_{y} = u_{z} ∙ v_{x} - u_{x} ∙ v_{y}

|u*⃗*∙v*⃗*|_{y} = ∙ - ∙

|u*⃗*∙v*⃗*|_{y} =

|u

|u

|u*⃗*∙v*⃗*|_{z} = u_{x} ∙ v_{y} - u_{y} ∙ v_{x}

|u*⃗*∙v*⃗*|_{z} = ∙ - ∙

|u*⃗*∙v*⃗*|_{z} =

|u

|u

|u*⃗*∙v*⃗*| = √*/**|u**⃗*∙v*⃗*|^{2}_{x} + |u*⃗*∙v*⃗*|^{2}_{y} + |u*⃗*∙v*⃗*|^{2}_{z}

|u*⃗*∙v*⃗*| = √*/* + +

|u*⃗*∙v*⃗*| =

|u

|u

cos θ = *u**⃗* ∙ v*⃗**/**|u**⃗*| ∙ |v*⃗*|

cos θ =*/* ∙

cos θ =

cos θ =

cos θ =

sin θ = *|u**⃗* ∙ v*⃗*|*/**|u**⃗*| ∙ |v*⃗*|

sin θ =*/* ∙

sin θ =

sin θ =

sin θ =

tan θ = *sin θ**/**cos θ*

tan θ =*/*

tan θ =

tan θ =

tan θ =

angle θ = arctan (tan θ)

angle θ = arctan ()

angle θ = ° (degrees)

angle θ = arctan (

angle θ =

You may also find the following Physics calculators useful.

- Hookes Law Spring Constant Calculator
- Mutual Inductance Calculator
- Coil Inductance Calculator
- Period Of Oscillations In A Shm Calculator
- Rydberg Equation Calculator
- Antenna Aperture Calculator
- Conservation Of Momentum In 2 D Calculator
- Rotational Velocity Of Star Calculator
- Line Of Sight Calculator
- 1 D Work Calculator
- Cosmic Velocities Calculator
- Hall Electrical Conductivity Calculator
- Gravitational Potential Energy Physics Calculator
- Uniform Motion Calculator
- De Broglie Wavelength Of Particle Calculator
- Partially Filled Horizontal Tank Volume Calculator
- Pipe Diameter Calculator
- Broad Crested Weir Calculator
- Height Of Liquid Rise In Capillary Tubes Calculator
- Impulse Calculator