Right Hand Rule Calculator

Calculator

Problem mode

Scalar multiplier

Charge sign

First vector x

First vector y

First vector z

Second vector x

Second vector y

Second vector z

Decimal precision

Coordinate guide: positive x points right, positive y points upward, and positive z points out of the page.

Formula Used

The main formula is the vector cross product:

A × B = <AyBz − AzBy, AzBx − AxBz, AxBy − AyBx>

The magnitude formula is:

|A × B| = |A||B|sin(θ)

The angle is found from:

cos(θ) = A · B / (|A||B|)

For magnetic force, the calculator uses q(v × B). For wire force, it uses I(L × B). For torque, it uses r × F.

How to Use This Calculator

Select the mode that matches your problem. Enter the first vector components. Enter the second vector components. Add a scalar when needed. Use negative charge only for magnetic force problems with negative particles. Press calculate. The result appears above the form. Use the export buttons to save your result.

Example Data Table

Mode	First vector	Second vector	Expected direction
A × B	<1, 0, 0>	<0, 1, 0>	Out of the page
A × B	<0, 1, 0>	<1, 0, 0>	Into the page
Torque	<2, 0, 0>	<0, 5, 0>	Positive z
Magnetic force	<0, 0, 3>	<1, 0, 0>	Positive y for positive charge

Right Hand Rule Calculator Guide

A right hand rule calculator helps you check direction fast. It is useful when a vector product decides an answer. Many physics and engineering tasks use this idea. Examples include torque, magnetic force, angular momentum, and force on a current wire.

The rule links two input directions to one output direction. Point your index finger along the first vector. Bend your middle finger toward the second vector. Your thumb shows the positive cross product direction. The calculator follows the same order. Changing the order changes the sign.

The core formula is A cross B. The component result is built from three paired differences. The x component is AyBz minus AzBy. The y component is AzBx minus AxBz. The z component is AxBy minus AyBx. Magnitude equals |A||B|sin theta. The angle comes from the dot product formula.

For magnetic force, the same cross product is used. A positive charge follows v cross B. A negative charge points the opposite way. A current wire follows L cross B. Torque follows r cross F. The tool lets you choose a mode, so the labels match the problem.

Use the signs carefully. Positive z is treated as out of the page. Negative z is into the page. Positive x points right. Negative x points left. Positive y points upward. Negative y points downward. If the result has mixed components, read the full unit vector.

This calculator also checks the angle between inputs. Parallel vectors produce zero cross product. Perpendicular vectors create the largest magnitude. The table gives sample cases for quick comparison. Exports help store lab notes or homework checks.

Start by selecting the problem mode. Enter the first vector components. Enter the second vector components. Choose the charge sign when magnetic force is selected. Press calculate. Read the dominant direction, components, magnitude, and steps. Download the CSV or PDF when you need a record.

Good results depend on consistent units. Use meters with newtons when solving torque. Use meters per second and tesla when solving magnetic force. Use any matching vector units for pure direction checks. Zero inputs are allowed, but they can make direction undefined. In that case, the calculator explains the zero result and avoids false direction claims clearly.

FAQs

What does the right hand rule find?

It finds the direction of a cross product. It is used for torque, magnetic force, angular momentum, and current wire force.

Which vector goes first?

Use the order shown in your formula. A × B is not the same as B × A. Reversing the order reverses the direction.

What does positive z mean?

Positive z means out of the page in this calculator. Negative z means into the page.

Can I use this for magnetic force?

Yes. Select magnetic force. Enter velocity as the first vector and magnetic field as the second vector.

Why does negative charge reverse direction?

Magnetic force equals q(v × B). A negative charge has a negative q value, so the force direction flips.

What if the result is zero?

A zero result means the vectors are parallel, opposite, or one vector has zero magnitude. The direction is undefined.

Do units matter for direction?

Direction mainly depends on signs and vector orientation. Magnitude needs consistent units for useful physical results.

Can I export my answer?

Yes. Use the CSV or PDF buttons after entering values. The exported file includes inputs, magnitude, angle, and direction.