Mathematics · Discrete Mathematics
Critical-Path Activity Free Float Calculator
Calculate activity free float from earliest successor start time and activity early finish time.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a−b with earliest successor start time=20 and activity early finish time=18.
- activity free float=2.
Understand Critical-Path Activity Free Float
One idea, three depths
Choose how deeply to explain Critical-Path Activity Free Float
Critical-Path Activity Free Float: Calculate activity free float from earliest successor start time and activity early finish time.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Critical-Path Activity Free Float to answer this question: calculate activity free float from earliest successor start time and activity early finish time? Enter earliest successor start time and activity early finish time; the calculator shows activity free float. For example: earliest successor start time=20 and activity early finish time=18 produce activity free float=2. The answer tells you activity free float.
Age 15Explain it to a 15-year-oldConnect it to the formula
Free float is the delay available before affecting the earliest start of a successor. This page evaluates the relationship directly. The rule is c=a−b. Its input values are earliest successor start time, activity early finish time, and the main result is activity free float. For example: earliest successor start time=20 and activity early finish time=18 produce activity free float=2.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated critical-path activity free float relation over the valid real-number domain stated below. The implemented relation is c=a−b, evaluated from earliest successor start time, activity early finish time to produce activity free float. Free float is the delay available before affecting the earliest start of a successor. This page evaluates the relationship directly. For multiple successors use the minimum eligible successor early start.
Inputs and valid domain
- earliest successor start time must be a finite real number.
- activity early finish time must be a finite real number.
Important boundary: For multiple successors use the minimum eligible successor early start.
The formula
c=a−b
How the calculator works through it
It substitutes earliest successor start time, activity early finish time into the formula and exposes every numerical step above. The main output is activity free float.
Read the result correctly
The activity free float is the direct answer to “calculate activity free float from earliest successor start time and activity early finish time.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
earliest successor start time=20 and activity early finish time=18 produce activity free float=2.
Where this model stops being reliable
For multiple successors use the minimum eligible successor early start.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Critical-Path Activity Free Float works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Critical-Path Activity Free Float uses c=a−b. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Sets, membership and finite collections
Sets provide the objects and membership rules that give Critical-Path Activity Free Float its discrete meaning.
Review this foundation about 6 min
Optional enrichment
- Ordered arrangements
Permutations connect Critical-Path Activity Free Float to systematic counting and arrangement problems.
Review this foundation about 5 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read earliest successor start time, activity early finish time.
- Evaluate the principal relationship: c=a−b.
- Return activity free float and check the domain conditions described above.
Python
from math import *
def critical_path_free_float_calculator(a, b) -> float:
return (a - b)
assert abs(critical_path_free_float_calculator(20, 18) - 2) < 1e-6 * max(1.0, abs(2))
C
#include <assert.h>
#include <math.h>
double critical_path_free_float_calculator(double a, double b) {
return (a - b);
}
int main(void) {
const double expected = 2;
const double actual = critical_path_free_float_calculator(20, 18);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double critical_path_free_float_calculator(double a, double b) {
return (a - b);
}
int main() {
constexpr double expected = 2;
const double actual = critical_path_free_float_calculator(20, 18);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double critical_path_free_float_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global critical_path_free_float_calculator
section .text
critical_path_free_float_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
subsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = critical_path_free_float_calculator(a, b)
result = (a - b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a - b);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Critical-Path Activity Free Float Calculator. MW SysArc Tools. https://math.mwsysarc.com/discrete-mathematics/critical-path-free-float-calculator
MLA 9
MW SysArc. “Critical-Path Activity Free Float Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/discrete-mathematics/critical-path-free-float-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Critical-Path Activity Free Float Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/discrete-mathematics/critical-path-free-float-calculator.
Harvard
MW SysArc (2026) ‘Critical-Path Activity Free Float Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/discrete-mathematics/critical-path-free-float-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_critical_path_free_float_calculator_2026,
author = {{MW SysArc}},
title = {Critical-Path Activity Free Float Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/discrete-mathematics/critical-path-free-float-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Critical-Path Activity Free Float Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/discrete-mathematics/critical-path-free-float-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Critical-Path Activity Free Float do?
Calculate activity free float from earliest successor start time and activity early finish time.
How does the Critical-Path Activity Free Float work?
The calculator applies c=a−b. Free float is the delay available before affecting the earliest start of a successor. This page evaluates the relationship directly.
What can I learn from the Critical-Path Activity Free Float?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .