Sqr Function

Returns a Double specifying the square root of a number.

Syntax

Sqr(number)

Parameters

number - Required. Double or any valid numeric expression greater than or equal to 0.

Return Value

Returns a Double containing the square root of the number.

Remarks

The Sqr function calculates the positive square root of a non-negative number. It's one of the fundamental mathematical functions in VB6 and is commonly used in geometric calculations, statistical analysis, and scientific applications.

Key characteristics: - Returns the positive (principal) square root only - Argument must be >= 0 (negative values cause Error 5) - Returns Double for maximum precision - Sqr(0) = 0 - Sqr(1) = 1 - Sqr(x) * Sqr(x) = x (within floating-point precision) - Inverse operation of squaring: Sqr(x^2) = x (for x >= 0)

Mathematical relationships: - Sqr(x * y) = Sqr(x) * Sqr(y) - Sqr(x / y) = Sqr(x) / Sqr(y) - Sqr(x^2) = Abs(x) - x^(1/2) = Sqr(x) - x^(1/n) can be calculated as x^(1/n) = Exp(Log(x) / n)

Typical Uses

Distance Calculations: Calculate distance between two points
Pythagorean Theorem: Find hypotenuse or sides of right triangles
Standard Deviation: Statistical calculations
Quadratic Equations: Solve equations using quadratic formula
Normalization: Normalize vectors and values
Root Mean Square: Calculate RMS values
Geometric Calculations: Circle, sphere, and other shape calculations
Physics Simulations: Velocity, acceleration, and energy calculations

Basic Examples

' Example 1: Calculate square root of a number
Dim result As Double
result = Sqr(25)
' Returns 5

' Example 2: Distance between two points (Pythagorean theorem)
Dim x1 As Double, y1 As Double
Dim x2 As Double, y2 As Double
Dim distance As Double

x1 = 0: y1 = 0
x2 = 3: y2 = 4
distance = Sqr((x2 - x1) ^ 2 + (y2 - y1) ^ 2)
' Returns 5

' Example 3: Calculate hypotenuse of right triangle
Dim sideA As Double
Dim sideB As Double
Dim hypotenuse As Double

sideA = 3
sideB = 4
hypotenuse = Sqr(sideA ^ 2 + sideB ^ 2)
' Returns 5

' Example 4: Quadratic formula
Dim a As Double, b As Double, c As Double
Dim discriminant As Double
Dim root1 As Double, root2 As Double

a = 1: b = -5: c = 6
discriminant = b ^ 2 - 4 * a * c

If discriminant >= 0 Then
root1 = (-b + Sqr(discriminant)) / (2 * a)
root2 = (-b - Sqr(discriminant)) / (2 * a)
End If

Common Patterns

Pattern 1: `CalculateDistance2D`

Calculate distance between two 2D points

Function CalculateDistance2D(x1 As Double, y1 As Double, _
x2 As Double, y2 As Double) As Double
Dim dx As Double
Dim dy As Double

dx = x2 - x1
dy = y2 - y1

CalculateDistance2D = Sqr(dx * dx + dy * dy)
End Function

Pattern 2: `CalculateDistance3D`

Calculate distance between two 3D points

Function CalculateDistance3D(x1 As Double, y1 As Double, z1 As Double, _
x2 As Double, y2 As Double, z2 As Double) As Double
Dim dx As Double, dy As Double, dz As Double

dx = x2 - x1
dy = y2 - y1
dz = z2 - z1

CalculateDistance3D = Sqr(dx * dx + dy * dy + dz * dz)
End Function

Pattern 3: `CalculateHypotenuse`

Calculate hypotenuse of right triangle

Function CalculateHypotenuse(sideA As Double, sideB As Double) As Double
CalculateHypotenuse = Sqr(sideA ^ 2 + sideB ^ 2)
End Function

Pattern 4: `CalculateStandardDeviation`

Calculate standard deviation of values

Function CalculateStandardDeviation(values() As Double) As Double
Dim i As Integer
Dim sum As Double
Dim mean As Double
Dim sumSquaredDiff As Double
Dim count As Integer

count = UBound(values) - LBound(values) + 1

' Calculate mean
sum = 0
For i = LBound(values) To UBound(values)
sum = sum + values(i)
Next i
mean = sum / count

' Calculate sum of squared differences
sumSquaredDiff = 0
For i = LBound(values) To UBound(values)
sumSquaredDiff = sumSquaredDiff + (values(i) - mean) ^ 2
Next i

CalculateStandardDeviation = Sqr(sumSquaredDiff / count)
End Function

Pattern 5: `NormalizeVector`

Normalize a 2D vector

Sub NormalizeVector(x As Double, y As Double)
Dim magnitude As Double

magnitude = Sqr(x * x + y * y)

If magnitude > 0 Then
x = x / magnitude
y = y / magnitude
End If
End Sub

Pattern 6: `CalculateRMS`

Calculate root mean square

Function CalculateRMS(values() As Double) As Double
Dim i As Integer
Dim sumSquares As Double
Dim count As Integer

count = UBound(values) - LBound(values) + 1
sumSquares = 0

For i = LBound(values) To UBound(values)
sumSquares = sumSquares + values(i) ^ 2
Next i

CalculateRMS = Sqr(sumSquares / count)
End Function

Pattern 7: `SolveQuadratic`

Solve quadratic equation ax² + bx + c = 0

Function SolveQuadratic(a As Double, b As Double, c As Double, _
root1 As Double, root2 As Double) As Boolean
Dim discriminant As Double

discriminant = b * b - 4 * a * c

If discriminant < 0 Then
SolveQuadratic = False
Exit Function
End If

root1 = (-b + Sqr(discriminant)) / (2 * a)
root2 = (-b - Sqr(discriminant)) / (2 * a)
SolveQuadratic = True
End Function

Pattern 8: `CalculateCircleRadius`

Calculate radius from area

Function CalculateCircleRadius(area As Double) As Double
Const PI As Double = 3.14159265358979
CalculateCircleRadius = Sqr(area / PI)
End Function

Pattern 9: `CalculateVelocity`

Calculate velocity from kinetic energy

Function CalculateVelocity(kineticEnergy As Double, mass As Double) As Double
' KE = 1/2 * m * v^2
' v = Sqr(2 * KE / m)
If mass > 0 Then
CalculateVelocity = Sqr(2 * kineticEnergy / mass)
Else
CalculateVelocity = 0
End If
End Function

Pattern 10: `IsPerfectSquare`

Check if number is a perfect square

Function IsPerfectSquare(n As Long) As Boolean
Dim sqrtValue As Double
Dim intValue As Long

If n < 0 Then
IsPerfectSquare = False
Exit Function
End If

sqrtValue = Sqr(n)
intValue = CLng(sqrtValue)
IsPerfectSquare = (intValue * intValue = n)
End Function

Advanced Usage

Example 1: `GeometryHelper` Class

Geometric calculations using Sqr

' Class: GeometryHelper

Public Function DistanceBetweenPoints(x1 As Double, y1 As Double, _
x2 As Double, y2 As Double) As Double
DistanceBetweenPoints = Sqr((x2 - x1) ^ 2 + (y2 - y1) ^ 2)
End Function

Public Function PointToLineDistance(px As Double, py As Double, _
x1 As Double, y1 As Double, _
x2 As Double, y2 As Double) As Double
' Distance from point to line segment
Dim A As Double, B As Double, C As Double

A = px - x1
B = py - y1
C = x2 - x1
Dim D As Double
D = y2 - y1

Dim dot As Double
dot = A * C + B * D
Dim lenSq As Double
lenSq = C * C + D * D

Dim param As Double
param = -1
If lenSq <> 0 Then param = dot / lenSq

Dim xx As Double, yy As Double

If param < 0 Then
xx = x1
yy = y1
ElseIf param > 1 Then
xx = x2
yy = y2
Else
xx = x1 + param * C
yy = y1 + param * D
End If

Dim dx As Double, dy As Double
dx = px - xx
dy = py - yy

PointToLineDistance = Sqr(dx * dx + dy * dy)
End Function

Public Function CircleArea(radius As Double) As Double
Const PI As Double = 3.14159265358979
CircleArea = PI * radius * radius
End Function

Public Function CircleRadiusFromArea(area As Double) As Double
Const PI As Double = 3.14159265358979
CircleRadiusFromArea = Sqr(area / PI)
End Function

Public Function SphereVolume(radius As Double) As Double
Const PI As Double = 3.14159265358979
SphereVolume = (4# / 3#) * PI * radius ^ 3
End Function

Public Function SphereRadiusFromVolume(volume As Double) As Double
Const PI As Double = 3.14159265358979
SphereRadiusFromVolume = ((3 * volume) / (4 * PI)) ^ (1# / 3#)
End Function

Example 2: `StatisticsCalculator` Class

Statistical calculations with Sqr

' Class: StatisticsCalculator
Private m_values() As Double
Private m_count As Integer

Public Sub AddValue(value As Double)
If m_count > UBound(m_values) Then
ReDim Preserve m_values(0 To m_count * 2)
End If
m_values(m_count) = value
m_count = m_count + 1
End Sub

Public Sub Clear()
m_count = 0
ReDim m_values(0 To 9)
End Sub

Private Sub Class_Initialize()
Clear
End Sub

Public Function GetMean() As Double
Dim sum As Double
Dim i As Integer

If m_count = 0 Then
GetMean = 0
Exit Function
End If

sum = 0
For i = 0 To m_count - 1
sum = sum + m_values(i)
Next i

GetMean = sum / m_count
End Function

Public Function GetStandardDeviation() As Double
Dim mean As Double
Dim sumSquaredDiff As Double
Dim i As Integer

If m_count = 0 Then
GetStandardDeviation = 0
Exit Function
End If

mean = GetMean()
sumSquaredDiff = 0

For i = 0 To m_count - 1
sumSquaredDiff = sumSquaredDiff + (m_values(i) - mean) ^ 2
Next i

GetStandardDeviation = Sqr(sumSquaredDiff / m_count)
End Function

Public Function GetVariance() As Double
Dim sd As Double
sd = GetStandardDeviation()
GetVariance = sd * sd
End Function

Public Function GetRMS() As Double
Dim sumSquares As Double
Dim i As Integer

If m_count = 0 Then
GetRMS = 0
Exit Function
End If

sumSquares = 0
For i = 0 To m_count - 1
sumSquares = sumSquares + m_values(i) ^ 2
Next i

GetRMS = Sqr(sumSquares / m_count)
End Function

Public Property Get Count() As Integer
Count = m_count
End Property

Example 3: `PhysicsEngine` Module

Physics calculations using Sqr

' Module: PhysicsEngine

Public Function CalculateVelocityFromEnergy(kineticEnergy As Double, _
mass As Double) As Double
' v = Sqr(2 * KE / m)
If mass > 0 Then
CalculateVelocityFromEnergy = Sqr(2 * kineticEnergy / mass)
Else
CalculateVelocityFromEnergy = 0
End If
End Function

Public Function CalculateEscapeVelocity(mass As Double, radius As Double) As Double
' v_escape = Sqr(2 * G * M / R)
Const G As Double = 6.674E-11  ' Gravitational constant
CalculateEscapeVelocity = Sqr(2 * G * mass / radius)
End Function

Public Function CalculatePeriod(length As Double) As Double
' Period of simple pendulum: T = 2π * Sqr(L/g)
Const PI As Double = 3.14159265358979
Const g As Double = 9.81  ' Gravity
CalculatePeriod = 2 * PI * Sqr(length / g)
End Function

Public Function CalculateFallTime(height As Double) As Double
' Time to fall from height: t = Sqr(2h/g)
Const g As Double = 9.81  ' Gravity
CalculateFallTime = Sqr(2 * height / g)
End Function

Public Function CalculateImpactVelocity(height As Double) As Double
' v = Sqr(2gh)
Const g As Double = 9.81  ' Gravity
CalculateImpactVelocity = Sqr(2 * g * height)
End Function

Public Function CalculateOrbitalVelocity(mass As Double, radius As Double) As Double
' v = Sqr(G * M / R)
Const G As Double = 6.674E-11  ' Gravitational constant
CalculateOrbitalVelocity = Sqr(G * mass / radius)
End Function

Example 4: `VectorMath` Module

Vector operations using Sqr

' Module: VectorMath

Public Function VectorMagnitude2D(x As Double, y As Double) As Double
VectorMagnitude2D = Sqr(x * x + y * y)
End Function

Public Function VectorMagnitude3D(x As Double, y As Double, z As Double) As Double
VectorMagnitude3D = Sqr(x * x + y * y + z * z)
End Function

Public Sub NormalizeVector2D(x As Double, y As Double)
Dim magnitude As Double
magnitude = VectorMagnitude2D(x, y)

If magnitude > 0 Then
x = x / magnitude
y = y / magnitude
End If
End Sub

Public Sub NormalizeVector3D(x As Double, y As Double, z As Double)
Dim magnitude As Double
magnitude = VectorMagnitude3D(x, y, z)

If magnitude > 0 Then
x = x / magnitude
y = y / magnitude
z = z / magnitude
End If
End Sub

Public Function DotProduct2D(x1 As Double, y1 As Double, _
x2 As Double, y2 As Double) As Double
DotProduct2D = x1 * x2 + y1 * y2
End Function

Public Function VectorDistance2D(x1 As Double, y1 As Double, _
x2 As Double, y2 As Double) As Double
VectorDistance2D = Sqr((x2 - x1) ^ 2 + (y2 - y1) ^ 2)
End Function

Public Function VectorAngleBetween(x1 As Double, y1 As Double, _
x2 As Double, y2 As Double) As Double
' Returns angle in radians
Dim dot As Double
Dim mag1 As Double, mag2 As Double

dot = DotProduct2D(x1, y1, x2, y2)
mag1 = VectorMagnitude2D(x1, y1)
mag2 = VectorMagnitude2D(x2, y2)

If mag1 > 0 And mag2 > 0 Then
VectorAngleBetween = Atn(Sqr(1 - (dot / (mag1 * mag2)) ^ 2) / (dot / (mag1 * mag2)))
Else
VectorAngleBetween = 0
End If
End Function

Error Handling

The Sqr function can generate the following errors:

Error 5 (Invalid procedure call or argument): If number is negative
Error 13 (Type mismatch): If argument is not numeric

Always validate inputs:

On Error Resume Next
If value >= 0 Then
result = Sqr(value)
If Err.Number <> 0 Then
MsgBox "Error calculating square root: " & Err.Description
End If
Else
MsgBox "Cannot calculate square root of negative number"
End If

Performance Considerations

Sqr is a relatively fast operation
Uses hardware floating-point unit when available
For repeated calculations, consider caching results
Sqr(x^2) is slower than Abs(x) for getting absolute value
For integer square roots, consider using Int(Sqr(x))

Best Practices

Validate Input: Always ensure argument is non-negative
Use for Distances: Ideal for Euclidean distance calculations
Combine with ^2: Use for Pythagorean theorem applications
Handle Zero: Remember Sqr(0) = 0 is valid
Precision Aware: Understand floating-point precision limits
Error Handling: Trap errors for negative inputs
Performance: Cache results when used repeatedly
Consider Abs: For Sqr(x^2), use Abs(x) instead
Document Units: Comment on units in physics calculations
Test Edge Cases: Test with 0, very small, and very large values

Operation	VB6 Function	Example	Result
Square root	Sqr(x)	Sqr(25)	5
Cube root	x^(1/3)	27^(1/3)	3
Nth root	x^(1/n)	16^(1/4)	2
Power	x^y	2^3	8
Absolute value	Abs(x)	Abs(-5)	5

Platform Considerations

Available in VB6, VBA (all versions)
Part of core mathematical functions
Uses IEEE 754 floating-point arithmetic
Consistent behavior across platforms
Hardware-accelerated on modern processors

Limitations

Cannot calculate square root of negative numbers (use complex number libraries)
Subject to floating-point precision limits (~15-17 significant digits)
Sqr(x)^2 may not exactly equal x due to rounding
Very large numbers may overflow Double range
Very small numbers may underflow to zero

Abs: Returns absolute value of a number
Exp: Returns e raised to a power
Log: Returns natural logarithm
^ operator: Raises number to a power (x^0.5 = Sqr(x))

Sqr Function

Syntax

Parameters

Return Value

Remarks

Typical Uses

Basic Examples

Common Patterns

Pattern 1: CalculateDistance2D

Pattern 2: CalculateDistance3D

Pattern 3: CalculateHypotenuse

Pattern 4: CalculateStandardDeviation

Pattern 5: NormalizeVector

Pattern 6: CalculateRMS

Pattern 7: SolveQuadratic

Pattern 8: CalculateCircleRadius

Pattern 9: CalculateVelocity

Pattern 10: IsPerfectSquare