### iPhone / iPad Scientific Calculator for Error / Uncertainty Propagation and Analysis

 ErrorCalc is a scientific calculator app for iPhone, iPad, iPod touch that is designed for error/uncertainty propagation and analysis of experimental data sets.  All values entered into the calculator can include error/uncertainty, which will be propagated during successive calculations. In addition to  ba sic arithmetic functions, trigonometric and exponential/logarithmic functions can be calculated. The app can also calculate both weighted and unweighted means/standard deviations for experimental data sets. In addition to standard algebraic entry mode (ALG), will allow Reverse Polish Notation (RPN) entry mode (which is common on HP Calculators).   There is also a Free version of ErrorCalc that allows uncertainties in Multiplication, Division, Addition and Subtraction of numbers.  Numbers can be written in scientific notation.                                                                                                 Entering Values Top line of screen (yellow background) shows status. Lower pair of lines (white and gray) are for values (upper line) and for error (lower line) The active entry line has white background To enter the value 9.8 with an uncertainty of 0.1 Touch upper display line (its background will be white) Then type 9.8 Touch lower display line for errors (which will then change to white leaving the upper line gray)   Then type 0.1 Alternately, press the ± label to toggle between value and error lines Touch ALG to toggle between ALGebraic and RPN modes -------- ALGebraic Mode Calculations --------- Example: To calculate  4±0.1 - 2±0.1 Enter the value 4 (in the upper of the pair of lines) Then touch the lower line and type in 0.1 for the error.   Next press the plus key Finally, type 2 in the upper line for the value Enter 0.1 in the lower line Pressing = gives a result of 2.0 ± 0.1414 ErrorCalc does not allow mixed mode operations such as multiplication followed by addition without equal sign Equations with several sequential Multiply/Divide or Add/Subtract are allowed without intermediate equal signs.      For Example:            3 / 4 * 2 / 5 = Gives 0.3         3 - 4 + 2 - 5 = Gives -4         3 / 4 * 2 + 5 Gives Error (since it is mixed mode once the + sign is pressed) Sample Mixed Mode Calculation: To calculate the value of sin(30±2 - 20±1) / (4.0±0.1 - 2.0±0.1) First calculate:  4±0.1 - 2±0.1  =   which gives 2.0 ± 0.1414 Store in memory using  Mem followed by MCl (if needed) and M+ to add to memory Next calculate 30±2 - 20±1 = which gives 10.0 ± 2.236 To take the sine, Set D/R rocker to D (Degrees) Press Func then Sin  which gives 0.17365 ± 0.03843 Finally press divide button and Mem MRcl to recall giving a final result of 0.0868 ± 0.0202 To Scroll Through Previous Values and Results Touch finger and drag up or down in the region of the screen near value and error displays. -------- RPN Mode Calculations --------- Example: To calculate  4±0.1 - 2±0.1 Enter the value 4 (in the upper of the pair of lines) Then touch the lower line and type in 0.1 for the error.   Next press the Enter key to push the value onto the stack Finally, type 2 in the upper line for the value Enter 0.1 in the lower line Pressing - subtracts gives a result of 2.0 ± 0.1414 Sample Mixed Mode Calculation: To calculate the value of sin(30±2 - 20±1) / (4.0±0.1 - 2.0±0.1) First calculate:  30±2 ENTER 20±1 - (Minus sign) which gives 10.0 ± 2.236 To take the sine, Set D/R rocker to D (Degrees) Press Func then Sin  which gives 0.17365 ± 0.03843 Press Enter to push this value to the stack Next calculate 4.0±0.1 Enter 2.0±0.1 - (Minus sign) which gives 2.0 ± 0.1414 Finally press divide button giving a final result of 0.0868 ± 0.0202 -------- Other Features --------- The Func button enables keys to allow calculation (with uncertainty) of trigonometric and exponential functions. The D/R toggle switches between Degrees and Radians for trig functions Ln calculates Natural Log Log calculates Common (base 10) Log" The Mem button allows values to be stored to memory, recalled and cleared.   (The Mem button will be bright red when a value is stored and dim red if memory is clear) M+ : Adds value (and error) to memory M- : Subtracts value from memory MClr : Clears Memory MRCl : Recalls Memory Value Prev and Next : Cycles through previous results Click : Turns Clicks on/off\ Ave : Enters the Average Mode (see below for details) Reset : Resets Calculator to its initial state Help : Enters Help Screen (can also use the "i" button) Statistics (Weighted and Unweighted)   On iPhone: To get to Average mode, Press Mem,  then Ave Enter Each Value then Press Data+ (to delete a point on iPad, use Data -) SCalc to Calculate statistics Press StatCl to Clear Statistics On iPhone, Press Exit to leave the statistics mode. For Unweighted Statistics, Do Not Include Errors The resulting calculation is the unweighted mean, and the Sample Standard Deviation Sample Data Set: 1, 2, 3  Gives the Result: Ave=2, StdDev=1 For Weighted Statistics, Include Error for Each Value Sample Data Set: 1±0.1, 2±0.2, 3±0.3 Gives the Result: Ave=1.3469, StdDev=0.0857 Contact Information:  Error.Calculator@gmail.com           © Thomas Huber, 2013 Since January 2013