Angle between two planes Calculator

Category	Math ↺
Math	3-D Geometry ↺
3-D-Geometry	Coordinate Geometry ↺
Coordinate-Geometry	Angle in 3D space ↺

✖Direction cosine with respect to x axis is the cosine of angle made by a line w.r.to x axis.ⓘ Direction cosine with respect to x axis [l]			+10% -10%
✖Direction cosine 2 with respect to x axis is the cosine of angle made by a line w.r.to x axis.ⓘ Direction cosine 2 with respect to x axis [l2]			+10% -10%
✖Direction cosine with respect to y axis is the cosine of angle made by a line w.r.to y axis.ⓘ Direction cosine with respect to y axis [m]			+10% -10%
✖Direction cosine 2 with respect to y axis is the cosine of angle made by a line w.r.to y axis.ⓘ Direction cosine 2 with respect to y axis [m2]			+10% -10%
✖Direction cosine with respect to z axis is the cosine of angle made by a line w.r.to z axis.ⓘ Direction cosine with respect to z axis [n]			+10% -10%
✖Direction cosine 2 with respect to z axis is the cosine of angle made by a line w.r.to z axis.ⓘ Direction cosine 2 with respect to z axis [n2]			+10% -10%

✖The angle A is one of the angles of a triangle.ⓘ Angle between two planes [∠A]

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Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 500+ more calculators!

Anamika Mittal

Vellore Institute of Technology (VIT), Bhopal

Anamika Mittal has verified this Calculator and 200+ more calculators!

< 11 Other formulas that you can solve using the same Inputs

Angle between two lines given direction cosines of that two lines w.r.to x, y & z axis

Angle A=acos ((Direction cosine with respect to x axis* Direction cosine 2 with respect to x axis)+(Direction cosine with respect to y axis* Direction cosine 2 with respect to y axis)+ (Direction cosine with respect to z axis* Direction cosine 2 with respect to z axis)) GO

Direction cosine of line2 w.r.to x axis given angle between line 1 & 2

Direction cosine 2 with respect to x axis= (cos(Angle A)-(Direction cosine with respect to y axis*Direction cosine 2 with respect to y axis)-(Direction cosine with respect to z axis*Direction cosine 2 with respect to z axis))/(Direction cosine with respect to x axis) GO

Direction cosine of line1 w.r.to x axis given angle between line 1 & 2

Direction cosine with respect to x axis= (cos(Angle A)-(Direction cosine with respect to y axis*Direction cosine 2 with respect to y axis)-(Direction cosine with respect to z axis*Direction cosine 2 with respect to z axis))/(Direction cosine 2 with respect to x axis) GO

Direction cosine of line2 w.r.to y axis given angle between line 1 & 2

Direction cosine 2 with respect to y axis= cos(Angle A)-(Direction cosine with respect to x axis*Direction cosine 2 with respect to x axis)-(Direction cosine with respect to z axis*Direction cosine 2 with respect to z axis)/(Direction cosine with respect to y axis) GO

Direction cosine of line2 w.r.to z axis given angle between line 1 & 2

Direction cosine 2 with respect to z axis= cos(Angle A)-(Direction cosine with respect to x axis*Direction cosine 2 with respect to x axis)-(Direction cosine with respect to y axis*Direction cosine 2 with respect to y axis)/(Direction cosine with respect to z axis) GO

Direction cosine of line1 w.r.to z axis given angle between line 1 & 2

Direction cosine with respect to z axis= cos(Angle A)-(Direction cosine with respect to x axis*Direction cosine 2 with respect to x axis)-(Direction cosine with respect to y axis*Direction cosine 2 with respect to y axis)/(Direction cosine 2 with respect to z axis) GO

Direction cosine of line1 w.r.to y axis given angle between line 1 & 2

Direction cosine with respect to y axis= cos(Angle A)-(Direction cosine with respect to x axis*Direction cosine 2 with respect to x axis)-(Direction cosine with respect to z axis*Direction cosine 2 with respect to z axis)/(Direction cosine 2 with respect to y axis) GO

Relation between direction cosines of coordinate axes

Relation between direction cosines=(Direction cosine with respect to x axis)^2+(Direction cosine with respect to y axis)^2+(Direction cosine with respect to z axis)^2 GO

Direction cosine w.r.to z axis given direction cosine w.r.to x and y axis

Direction cosine with respect to z axis= sqrt(1-(Direction cosine with respect to x axis)^2- (Direction cosine with respect to y axis)^2) GO

Direction cosine w.r.to y axis given direction cosine w.r.to x and z axis

Direction cosine with respect to y axis= sqrt(1-(Direction cosine with respect to x axis)^2- (Direction cosine with respect to z axis)^2) GO

Direction cosine w.r.to x axis given direction cosine w.r.to y and z axis

Direction cosine with respect to x axis= sqrt(1-(Direction cosine with respect to y axis)^2- (Direction cosine with respect to z axis)^2) GO

< 11 Other formulas that calculate the same Output

Angle between two lines given direction cosines of that two lines w.r.to x, y & z axis

Angle of intersection between two circles

Angle A=arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between two origin)^2))/(2*Radius 1*Radius 2)) GO

Acute angle of a rhombus if given both diagonals

Angle A=asin((2*Diagonal 1*Diagonal 2)/((Diagonal 1^2)+(Diagonal 2^2))) GO

Obtuse angle of rhombus if given both diagonal

Angle A=asin((2*Diagonal 1*Diagonal 2)/((Diagonal 1^2)+(Diagonal 2^2))) GO

Acute angle of rhombus given larger diagonal and side

Angle A=(arccos(((Diagonal 1)^2)/(2*(Side of rhombus )^2))-1) GO

One-half obtuse angles in a rhombus if given both diagonals

Angle A=2*(arctan(Diagonal 1/Diagonal 2)) GO

One-half acute angles in a rhombus if given both diagonals

Angle A=2*(arctan(Diagonal 2/Diagonal 1)) GO

Obtuse angle of a rhombus if given area and side

Angle A=asin(Area/Side^2) GO

Acute angle of a rhombus if given area and side

Angle A=asin(Area/Side^2) GO

Angle on the remaining part of the circumference when another angle on same chord is given

Angle A=1*Angle B GO

Angle at another point on circumference when angle on an arc is given

Angle A=1*Angle B GO

Angle between two planes Formula

Angle A=acos(((Direction cosine with respect to x axis*Direction cosine 2 with respect to x axis)+(Direction cosine with respect to y axis*Direction cosine 2 with respect to y axis)+(Direction cosine with respect to z axis*Direction cosine 2 with respect to z axis))/(sqrt((Direction cosine with respect to x axis)^2+(Direction cosine with respect to y axis)^2+(Direction cosine with respect to z axis)^2)* sqrt((Direction cosine 2 with respect to x axis)^2+(Direction cosine 2 with respect to y axis)^2+(Direction cosine 2 with respect to z axis)^2)))
∠A=acos(((l*l2)+(m*m2)+(n*n2))/(sqrt((l)^2+(m)^2+(n)^2)* sqrt((l2)^2+(m2)^2+(n2)^2)))

More formulas

Angle between two lines given direction cosines of that two lines w.r.to x, y & z axis GO

angle made by direction cosines of two lines in sine form GO

angle between two lines given direction ratios of that two lines w.r.to x, y & z axis GO

Angle between line and plane given coefficients of line and plane GO

What are direction cosines?

Direction cosines of a vector are the cosines of the angles between the vector and the three coordinate axes. Equivalently, they are the contributions of each component of the basis to a unit vector in that direction.

How to Calculate Angle between two planes?

Angle between two planes calculator uses Angle A=acos(((Direction cosine with respect to x axis*Direction cosine 2 with respect to x axis)+(Direction cosine with respect to y axis*Direction cosine 2 with respect to y axis)+(Direction cosine with respect to z axis*Direction cosine 2 with respect to z axis))/(sqrt((Direction cosine with respect to x axis)^2+(Direction cosine with respect to y axis)^2+(Direction cosine with respect to z axis)^2)* sqrt((Direction cosine 2 with respect to x axis)^2+(Direction cosine 2 with respect to y axis)^2+(Direction cosine 2 with respect to z axis)^2))) to calculate the Angle A, The Angle between two planes formula is defined as as the angle between the normal to them from any point. Angle A and is denoted by ∠A symbol.

How to calculate Angle between two planes using this online calculator? To use this online calculator for Angle between two planes, enter Direction cosine with respect to x axis (l), Direction cosine 2 with respect to x axis (l2), Direction cosine with respect to y axis (m), Direction cosine 2 with respect to y axis (m2), Direction cosine with respect to z axis (n) and Direction cosine 2 with respect to z axis (n2) and hit the calculate button. Here is how the Angle between two planes calculation can be explained with given input values -> 19.47122 = acos(((1*0.1)+(1*0.2)+(1*0.1))/(sqrt((1)^2+(1)^2+(1)^2)* sqrt((0.1)^2+(0.2)^2+(0.1)^2))).

FAQ

What is Angle between two planes?

The Angle between two planes formula is defined as as the angle between the normal to them from any point and is represented as ∠A=acos(((l*l2)+(m*m2)+(n*n2))/(sqrt((l)^2+(m)^2+(n)^2)* sqrt((l2)^2+(m2)^2+(n2)^2))) or Angle A=acos(((Direction cosine with respect to x axis*Direction cosine 2 with respect to x axis)+(Direction cosine with respect to y axis*Direction cosine 2 with respect to y axis)+(Direction cosine with respect to z axis*Direction cosine 2 with respect to z axis))/(sqrt((Direction cosine with respect to x axis)^2+(Direction cosine with respect to y axis)^2+(Direction cosine with respect to z axis)^2)* sqrt((Direction cosine 2 with respect to x axis)^2+(Direction cosine 2 with respect to y axis)^2+(Direction cosine 2 with respect to z axis)^2))). Direction cosine with respect to x axis is the cosine of angle made by a line w.r.to x axis, Direction cosine 2 with respect to x axis is the cosine of angle made by a line w.r.to x axis, Direction cosine with respect to y axis is the cosine of angle made by a line w.r.to y axis, Direction cosine 2 with respect to y axis is the cosine of angle made by a line w.r.to y axis, Direction cosine with respect to z axis is the cosine of angle made by a line w.r.to z axis and Direction cosine 2 with respect to z axis is the cosine of angle made by a line w.r.to z axis.

How to calculate Angle between two planes?

The Angle between two planes formula is defined as as the angle between the normal to them from any point is calculated using Angle A=acos(((Direction cosine with respect to x axis*Direction cosine 2 with respect to x axis)+(Direction cosine with respect to y axis*Direction cosine 2 with respect to y axis)+(Direction cosine with respect to z axis*Direction cosine 2 with respect to z axis))/(sqrt((Direction cosine with respect to x axis)^2+(Direction cosine with respect to y axis)^2+(Direction cosine with respect to z axis)^2)* sqrt((Direction cosine 2 with respect to x axis)^2+(Direction cosine 2 with respect to y axis)^2+(Direction cosine 2 with respect to z axis)^2))). To calculate Angle between two planes, you need Direction cosine with respect to x axis (l), Direction cosine 2 with respect to x axis (l2), Direction cosine with respect to y axis (m), Direction cosine 2 with respect to y axis (m2), Direction cosine with respect to z axis (n) and Direction cosine 2 with respect to z axis (n2). With our tool, you need to enter the respective value for Direction cosine with respect to x axis, Direction cosine 2 with respect to x axis, Direction cosine with respect to y axis, Direction cosine 2 with respect to y axis, Direction cosine with respect to z axis and Direction cosine 2 with respect to z axis and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Angle A?

In this formula, Angle A uses Direction cosine with respect to x axis, Direction cosine 2 with respect to x axis, Direction cosine with respect to y axis, Direction cosine 2 with respect to y axis, Direction cosine with respect to z axis and Direction cosine 2 with respect to z axis. We can use 11 other way(s) to calculate the same, which is/are as follows -

Angle A=1*Angle B
Angle A=1*Angle B
Angle A=(arccos(((Diagonal 1)^2)/(2*(Side of rhombus )^2))-1)
Angle A=arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between two origin)^2))/(2*Radius 1*Radius 2))
Angle A=asin((2*Diagonal 1*Diagonal 2)/((Diagonal 1^2)+(Diagonal 2^2)))
Angle A=asin((2*Diagonal 1*Diagonal 2)/((Diagonal 1^2)+(Diagonal 2^2)))
Angle A=asin(Area/Side^2)
Angle A=asin(Area/Side^2)
Angle A=2*(arctan(Diagonal 2/Diagonal 1))
Angle A=2*(arctan(Diagonal 1/Diagonal 2))
Angle A=acos ((Direction cosine with respect to x axis* Direction cosine 2 with respect to x axis)+(Direction cosine with respect to y axis* Direction cosine 2 with respect to y axis)+ (Direction cosine with respect to z axis* Direction cosine 2 with respect to z axis))

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