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Using a script, is there any way I can copy the current results of this RAND function into another cell on the sheet?

No, there isn't.

The following script should add the value of B2 to C2, but instead adds a new calculated value.

function freeze1(){
  var s = SpreadsheetApp.getActiveSheet();
  var v = s.getRange("B2").getValue();
  s.getRange("C2").setValue(v);
}

The following script should add the value of B2 to the active range, but it adds a new calculated value

function freeze2(){
  var s = SpreadsheetApp.getActiveSheet();
  var v = s.getRange("B2").getValue();
  var t = SpreadsheetApp.getActiveRange();
  t.setValue(v);
}

On both cases, a third value is calculated "after" the script runs.

Using a script, is there any way I can copy the current results of this RAND function into another cell on the sheet?

No, there isn't.

The following script should add the value of B2 to C2, but instead adds a new calculated value.

function freeze1(){
  var s = SpreadsheetApp.getActiveSheet();
  var v = s.getRange("B2").getValue();
  s.getRange("C2").setValue(v);
}

The following script should add the value of B2 to the active range, but it adds a new calculated value

function freeze2(){
  var s = SpreadsheetApp.getActiveSheet();
  var v = s.getRange("B2").getValue();
  var t = SpreadsheetApp.getActiveRange();
  t.setValue(v);
}

On both cases, a third value is calculated "after" the script runs.

An alternative could be the use of a script to calculate the random number instead of a built-in RANDOM() spreadsheet function. The JavaScript command is Math.random().

Using a script, is there any way I can copy the current results of this RAND function into another cell on the sheet?

The following script will add the value of B2 to C2

function freeze1(){
  var s = SpreadsheetApp.getActiveSheet();
  var v = s.getRange("B2").getValue();
  s.getRange("C2").setValue(v);
}

The following script will add the value of B2 to the active range

function freeze2(){
  var s = SpreadsheetApp.getActiveSheet();
  var v = s.getRange("B2").getValue();
  var t = SpreadsheetApp.getActiveRange();
  t.setValue(v);
}

Using a script, is there any way I can copy the current results of this RAND function into another cell on the sheet?

No, there isn't.

The following script should add the value of B2 to C2, but instead adds a new calculated value.

function freeze1(){
  var s = SpreadsheetApp.getActiveSheet();
  var v = s.getRange("B2").getValue();
  s.getRange("C2").setValue(v);
}

The following script should add the value of B2 to the active range, but it adds a new calculated value

function freeze2(){
  var s = SpreadsheetApp.getActiveSheet();
  var v = s.getRange("B2").getValue();
  var t = SpreadsheetApp.getActiveRange();
  t.setValue(v);
}

On both cases, a third value is calculated "after" the script runs.

Using a script, is there any way I can copy the current results of this RAND function into another cell on the sheet?

The following script will add the value of B2 to C2

function freeze(){
  var s = SpreadsheetApp.getActiveSheet();
  var v = s.getRange("B2").getValue();
  var t = s.getRange("C2").setValue(v);
}

Using a script, is there any way I can copy the current results of this RAND function into another cell on the sheet?

The following script will add the value of B2 to C2

function freeze1(){
  var s = SpreadsheetApp.getActiveSheet();
  var v = s.getRange("B2").getValue();
  s.getRange("C2").setValue(v);
}

The following script will add the value of B2 to the active range

function freeze2(){
  var s = SpreadsheetApp.getActiveSheet();
  var v = s.getRange("B2").getValue();
  var t = SpreadsheetApp.getActiveRange();
  t.setValue(v);
}