Mathematics · Probability
Weibull Survival from Cumulative Hazard Calculator
Calculate survival probability from unit initial survival and weibull cumulative hazard.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=ae^(−b) with unit initial survival=1 and Weibull cumulative hazard=1.4.
- survival probability=0.2465969639416065.
Understand Weibull Survival from Cumulative Hazard
One idea, three depths
Choose how deeply to explain Weibull Survival from Cumulative Hazard
Weibull Survival from Cumulative Hazard: Calculate survival probability from unit initial survival and weibull cumulative hazard.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Weibull Survival from Cumulative Hazard to answer this question: calculate survival probability from unit initial survival and weibull cumulative hazard? Enter unit initial survival and Weibull cumulative hazard; the calculator shows survival probability. For example: unit initial survival=1 and Weibull cumulative hazard=1.4 produce survival probability=0.2465969639416065. The answer tells you survival probability.
Age 15Explain it to a 15-year-oldConnect it to the formula
Weibull survival equals exp of minus cumulative hazard. This page evaluates the relationship directly. The rule is c=ae^(−b). Its input values are unit initial survival, Weibull cumulative hazard, and the main result is survival probability. For example: unit initial survival=1 and Weibull cumulative hazard=1.4 produce survival probability=0.2465969639416065.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated weibull survival from cumulative hazard relation over the valid real-number domain stated below. The implemented relation is c=ae^(−b), evaluated from unit initial survival, Weibull cumulative hazard to produce survival probability. Weibull survival equals exp of minus cumulative hazard. This page evaluates the relationship directly. The cumulative hazard is nonnegative, so survival stays between zero and one.
Inputs and valid domain
- unit initial survival must be a finite real number.
- Weibull cumulative hazard must be a finite real number.
Important boundary: The cumulative hazard is nonnegative, so survival stays between zero and one.
The formula
c=ae^(−b)
How the calculator works through it
It substitutes unit initial survival, Weibull cumulative hazard into the formula and exposes every numerical step above. The main output is survival probability.
Read the result correctly
The survival probability is the direct answer to “calculate survival probability from unit initial survival and weibull cumulative hazard.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
unit initial survival=1 and Weibull cumulative hazard=1.4 produce survival probability=0.2465969639416065.
Where this model stops being reliable
The cumulative hazard is nonnegative, so survival stays between zero and one.
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 Weibull Survival from Cumulative Hazard works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Weibull Survival from Cumulative Hazard uses c=ae^(−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
- Probability as a modelled proportion
Probability rules are needed to interpret what the Weibull Survival from Cumulative Hazard result says about possible outcomes.
Review this foundation about 5 min
Optional enrichment
- Ordered arrangements
Counting ordered arrangements can extend Weibull Survival from Cumulative Hazard to more detailed sample spaces and event models.
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 unit initial survival, Weibull cumulative hazard.
- Evaluate the principal relationship: c=ae^(−b).
- Return survival probability and check the domain conditions described above.
Python
from math import *
def weibull_survival_from_hazard_calculator(a, b) -> float:
return (a * exp((-b)))
assert abs(weibull_survival_from_hazard_calculator(1, 1.4) - 0.2465969639416065) < 1e-6 * max(1.0, abs(0.2465969639416065))
C
#include <assert.h>
#include <math.h>
double weibull_survival_from_hazard_calculator(double a, double b) {
return (a * exp((-b)));
}
int main(void) {
const double expected = 0.2465969639416065;
const double actual = weibull_survival_from_hazard_calculator(1, 1.4);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double weibull_survival_from_hazard_calculator(double a, double b) {
return (a * std::exp((-b)));
}
int main() {
constexpr double expected = 0.2465969639416065;
const double actual = weibull_survival_from_hazard_calculator(1, 1.4);
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 weibull_survival_from_hazard_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern exp
global weibull_survival_from_hazard_calculator
section .text
weibull_survival_from_hazard_calculator:
push rbp
mov rbp, rsp
sub rsp, 48
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
pxor xmm0, xmm0
subsd xmm0, [rbp-16]
movsd [rbp-40], xmm0
movsd xmm0, [rbp-40]
call exp wrt ..plt
movsd [rbp-32], xmm0
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-32]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = weibull_survival_from_hazard_calculator(a, b)
result = (a * exp((-b)));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a * Exp[(-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.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Introductory Statistics 2e
Read the free OpenStax statistics textbookCite this book
- APA 7
- Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
- MLA 9
- Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
- Chicago author-date
- Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
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). Weibull Survival from Cumulative Hazard Calculator. MW SysArc Tools. https://math.mwsysarc.com/probability/weibull-survival-from-hazard-calculator
MLA 9
MW SysArc. “Weibull Survival from Cumulative Hazard Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/probability/weibull-survival-from-hazard-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Weibull Survival from Cumulative Hazard Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/probability/weibull-survival-from-hazard-calculator.
Harvard
MW SysArc (2026) ‘Weibull Survival from Cumulative Hazard Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/probability/weibull-survival-from-hazard-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_weibull_survival_from_hazard_calculator_2026,
author = {{MW SysArc}},
title = {Weibull Survival from Cumulative Hazard Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/probability/weibull-survival-from-hazard-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Weibull Survival from Cumulative Hazard Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/probability/weibull-survival-from-hazard-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Weibull Survival from Cumulative Hazard do?
Calculate survival probability from unit initial survival and weibull cumulative hazard.
How does the Weibull Survival from Cumulative Hazard work?
The calculator applies c=ae^(−b). Weibull survival equals exp of minus cumulative hazard. This page evaluates the relationship directly.
What can I learn from the Weibull Survival from Cumulative Hazard?
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 .