business kpi API Reference

Business KPIs Module

This module provides functions for calculating various business metrics commonly used in SaaS and subscription-based businesses.

annual_recurring_revenue(paying_customers, avg_revenue_per_customer)

Calculate Annual Recurring Revenue (ARR).

ARR is the value of the recurring revenue of a business's term subscriptions normalized for a single calendar year.

Parameters:

Name	Type	Description	Default
paying_customers	array - like	Number of paying customers	required
avg_revenue_per_customer	array - like	Average revenue per customer per month	required

Returns:

Type	Description
float or ndarray	Annual Recurring Revenue

Examples:

>>> annual_recurring_revenue(100, 50)
60000.0

average_revenue_per_paying_user(total_revenue, paying_users)

Calculate Average Revenue Per Paying User (ARPPU).

ARPPU measures the average revenue generated per paying user or customer.

Parameters:

Name	Type	Description	Default
total_revenue	array - like	Total revenue for the period	required
paying_users	array - like	Number of paying users or customers	required

Returns:

Type	Description
float or ndarray	Average Revenue Per Paying User

Examples:

>>> average_revenue_per_paying_user(10000, 200)
50.0

average_revenue_per_user(total_revenue, total_users)

Calculate Average Revenue Per User (ARPU).

ARPU measures the average revenue generated per user or customer.

Parameters:

Name	Type	Description	Default
total_revenue	array - like	Total revenue for the period	required
total_users	array - like	Total number of users or customers	required

Returns:

Type	Description
float or ndarray	Average Revenue Per User

Examples:

>>> average_revenue_per_user(10000, 500)
20.0

burn_rate(starting_capital, ending_capital, months)

Calculate Monthly Burn Rate.

Burn Rate is the rate at which a company is losing money.

Parameters:

Name	Type	Description	Default
starting_capital	array - like	Capital at the start of the period	required
ending_capital	array - like	Capital at the end of the period	required
months	array - like	Number of months in the period	required

Returns:

Type	Description
float or ndarray	Monthly Burn Rate

Examples:

>>> burn_rate(100000, 70000, 6)
5000.0

churn_rate(customers_start, customers_end, new_customers)

Calculate customer churn rate.

Churn rate is the percentage of customers who stop using your product or service during a given time period.

Parameters:

Name	Type	Description	Default
customers_start	array - like	Number of customers at the start of the period	required
customers_end	array - like	Number of customers at the end of the period	required
new_customers	array - like	Number of new customers acquired during the period	required

Returns:

Type	Description
float or ndarray	Churn rate as a percentage

Examples:

>>> churn_rate(100, 90, 10)
20.0

conversion_rate(conversions, total_visitors)

Calculate Conversion Rate.

Conversion Rate is the percentage of visitors who take a desired action.

Parameters:

Name	Type	Description	Default
conversions	array - like	Number of conversions (desired actions taken)	required
total_visitors	array - like	Total number of visitors or users	required

Returns:

Type	Description
float or ndarray	Conversion Rate as a percentage

Examples:

>>> conversion_rate(50, 1000)
5.0

customer_acquisition_cost(marketing_costs, sales_costs, new_customers)

Calculate Customer Acquisition Cost (CAC).

CAC is the cost of convincing a potential customer to buy a product or service.

Parameters:

Name	Type	Description	Default
marketing_costs	array - like	Total marketing costs for the period	required
sales_costs	array - like	Total sales costs for the period	required
new_customers	array - like	Number of new customers acquired during the period	required

Returns:

Type	Description
float or ndarray	Customer Acquisition Cost

Examples:

>>> customer_acquisition_cost(5000, 3000, 100)
80.0

customer_effort_score(effort_ratings, max_rating=7)

Calculate Customer Effort Score (CES).

CES measures how much effort a customer has to exert to use a product or service. Lower scores are better.

Parameters:

Name	Type	Description	Default
effort_ratings	array - like	Array of customer effort ratings	required
max_rating	array - like	Maximum possible rating value	7

Returns:

Type	Description
float or ndarray	Customer Effort Score (average)

Examples:

>>> customer_effort_score([2, 3, 1, 2, 4])
2.4

customer_engagement_score(active_days, total_days)

Calculate Customer Engagement Score.

Customer Engagement Score measures how actively customers are using a product or service.

Parameters:

Name	Type	Description	Default
active_days	array - like	Number of days the customer was active	required
total_days	array - like	Total number of days in the period	required

Returns:

Type	Description
float or ndarray	Customer Engagement Score as a percentage

Examples:

>>> customer_engagement_score(15, 30)
50.0

customer_lifetime_value(avg_revenue_per_customer, gross_margin, churn_rate_value, discount_rate=10.0)

Calculate Customer Lifetime Value (CLV).

CLV is the total worth to a business of a customer over the whole period of their relationship.

Parameters:

Name	Type	Description	Default
avg_revenue_per_customer	array - like	Average revenue per customer per period (e.g., monthly)	required
gross_margin	array - like	Gross margin percentage (0-100)	required
churn_rate_value	array - like	Churn rate percentage (0-100)	required
discount_rate	array - like	Annual discount rate for future cash flows (0-100)	10.0

Returns:

Type	Description
float or ndarray	Customer Lifetime Value

Examples:

>>> customer_lifetime_value(100, 70, 5, 10)
466.67

customer_satisfaction_score(satisfaction_ratings, max_rating=5)

Calculate Customer Satisfaction Score (CSAT).

CSAT measures how satisfied customers are with a product, service, or interaction.

Parameters:

Name	Type	Description	Default
satisfaction_ratings	array - like	Array of customer satisfaction ratings	required
max_rating	array - like	Maximum possible rating value	5

Returns:

Type	Description
float or ndarray	Customer Satisfaction Score as a percentage

Examples:

>>> customer_satisfaction_score([4, 5, 3, 5, 4])
84.0

daily_active_users_ratio(daily_active_users, total_users)

Calculate Daily Active Users (DAU) Ratio.

DAU Ratio measures the percentage of total users who are active on a daily basis.

Parameters:

Name	Type	Description	Default
daily_active_users	array - like	Number of daily active users	required
total_users	array - like	Total number of users	required

Returns:

Type	Description
float or ndarray	Daily Active Users Ratio as a percentage

Examples:

>>> daily_active_users_ratio(500, 2000)
25.0

expansion_revenue_rate(upsell_revenue, cross_sell_revenue, revenue_start)

Calculate Expansion Revenue Rate.

Expansion Revenue Rate is the percentage of additional revenue generated from existing customers.

Parameters:

Name	Type	Description	Default
upsell_revenue	array - like	Revenue from upselling to existing customers	required
cross_sell_revenue	array - like	Revenue from cross-selling to existing customers	required
revenue_start	array - like	Revenue at the start of the period	required

Returns:

Type	Description
float or ndarray	Expansion Revenue Rate as a percentage

Examples:

>>> expansion_revenue_rate(1000, 500, 10000)
15.0

feature_adoption_rate(users_adopting_feature, total_users)

Calculate Feature Adoption Rate.

Feature Adoption Rate measures the percentage of users who adopt a specific feature.

Parameters:

Name	Type	Description	Default
users_adopting_feature	array - like	Number of users who adopted the feature	required
total_users	array - like	Total number of users	required

Returns:

Type	Description
float or ndarray	Feature Adoption Rate as a percentage

Examples:

>>> feature_adoption_rate(300, 1000)
30.0

gross_margin(revenue, cost_of_goods_sold)

Calculate Gross Margin.

Gross Margin is the percentage of revenue that exceeds the cost of goods sold.

Parameters:

Name	Type	Description	Default
revenue	array - like	Total revenue	required
cost_of_goods_sold	array - like	Cost of goods sold	required

Returns:

Type	Description
float or ndarray	Gross Margin as a percentage

Examples:

>>> gross_margin(10000, 3000)
70.0

ltv_cac_ratio(ltv, cac)

Calculate LTV:CAC Ratio.

LTV:CAC Ratio is a metric that compares the lifetime value of a customer to the cost of acquiring that customer.

Parameters:

Name	Type	Description	Default
ltv	array - like	Customer Lifetime Value	required
cac	array - like	Customer Acquisition Cost	required

Returns:

Type	Description
float or ndarray	LTV:CAC Ratio

Examples:

>>> ltv_cac_ratio(1000, 200)
5.0

monthly_active_users_ratio(monthly_active_users, total_users)

Calculate Monthly Active Users (MAU) Ratio.

MAU Ratio measures the percentage of total users who are active on a monthly basis.

Parameters:

Name	Type	Description	Default
monthly_active_users	array - like	Number of monthly active users	required
total_users	array - like	Total number of users	required

Returns:

Type	Description
float or ndarray	Monthly Active Users Ratio as a percentage

Examples:

>>> monthly_active_users_ratio(1500, 2000)
75.0

monthly_recurring_revenue(paying_customers, avg_revenue_per_customer)

Calculate Monthly Recurring Revenue (MRR).

MRR is the predictable total revenue generated by all the active subscriptions in a month.

Parameters:

Name	Type	Description	Default
paying_customers	array - like	Number of paying customers	required
avg_revenue_per_customer	array - like	Average revenue per customer per month	required

Returns:

Type	Description
float or ndarray	Monthly Recurring Revenue

Examples:

>>> monthly_recurring_revenue(100, 50)
5000.0

net_promoter_score(promoters, detractors, total_respondents)

Calculate Net Promoter Score (NPS).

NPS measures customer experience and predicts business growth.

Parameters:

Name	Type	Description	Default
promoters	array - like	Number of promoters (customers who rated 9-10)	required
detractors	array - like	Number of detractors (customers who rated 0-6)	required
total_respondents	array - like	Total number of survey respondents	required

Returns:

Type	Description
float or ndarray	Net Promoter Score (ranges from -100 to 100)

Examples:

>>> net_promoter_score(70, 10, 100)
60.0

payback_period(cac, avg_monthly_revenue, gross_margin)

Calculate CAC Payback Period in months.

CAC Payback Period is the number of months it takes to recover the cost of acquiring a customer.

Parameters:

Name	Type	Description	Default
cac	array - like	Customer Acquisition Cost	required
avg_monthly_revenue	array - like	Average monthly revenue per customer	required
gross_margin	array - like	Gross margin percentage (0-100)	required

Returns:

Type	Description
float or ndarray	CAC Payback Period in months

Examples:

>>> payback_period(1000, 100, 70)
14.29

retention_rate(customers_start, customers_end, new_customers)

Calculate customer retention rate.

Retention rate is the percentage of customers who remain with your product or service over a given time period.

Parameters:

Name	Type	Description	Default
customers_start	array - like	Number of customers at the start of the period	required
customers_end	array - like	Number of customers at the end of the period	required
new_customers	array - like	Number of new customers acquired during the period	required

Returns:

Type	Description
float or ndarray	Retention rate as a percentage

Examples:

>>> retention_rate(100, 90, 10)
80.0

revenue_churn_rate(revenue_start, revenue_end, new_revenue)

Calculate Revenue Churn Rate.

Revenue Churn Rate is the percentage of revenue lost from existing customers in a given period.

Parameters:

Name	Type	Description	Default
revenue_start	array - like	Revenue at the start of the period	required
revenue_end	array - like	Revenue at the end of the period	required
new_revenue	array - like	New revenue acquired during the period	required

Returns:

Type	Description
float or ndarray	Revenue Churn Rate as a percentage

Examples:

>>> revenue_churn_rate(10000, 9500, 1000)
15.0

roi(revenue, costs)

Calculate Return on Investment (ROI).

ROI measures the return on an investment relative to its cost.

Parameters:

Name	Type	Description	Default
revenue	array - like	Revenue or return from the investment	required
costs	array - like	Cost of the investment	required

Returns:

Type	Description
float or ndarray	Return on Investment as a percentage

Examples:

>>> roi(150, 100)
50.0
>>> roi([150, 200, 250], [100, 120, 150])
array([50., 66.67, 66.67])

runway(current_capital, monthly_burn_rate)

Calculate Runway in months.

Runway is the amount of time a company has before it runs out of money.

Parameters:

Name	Type	Description	Default
current_capital	array - like	Current capital	required
monthly_burn_rate	array - like	Monthly burn rate	required

Returns:

Type	Description
float or ndarray	Runway in months

Examples:

>>> runway(100000, 5000)
20.0

stickiness_ratio(daily_active_users, monthly_active_users)

Calculate Stickiness Ratio (DAU/MAU).

Stickiness Ratio measures how frequently active users engage with a product.

Parameters:

Name	Type	Description	Default
daily_active_users	array - like	Number of daily active users	required
monthly_active_users	array - like	Number of monthly active users	required

Returns:

Type	Description
float or ndarray	Stickiness Ratio as a percentage

Examples:

>>> stickiness_ratio(500, 1500)
33.33

time_to_value(onboarding_time, setup_time, learning_time)

Calculate Time to Value (TTV).

Time to Value is the amount of time it takes for a customer to realize value from a product.

Parameters:

Name	Type	Description	Default
onboarding_time	array - like	Time spent on onboarding	required
setup_time	array - like	Time spent on setup	required
learning_time	array - like	Time spent on learning	required

Returns:

Type	Description
float or ndarray	Time to Value

Examples:

>>> time_to_value(2, 3, 5)
10.0

virality_coefficient(new_users, invites_sent, total_users)

Calculate Virality Coefficient (K-factor).

Virality Coefficient measures how many new users each existing user brings in.

Parameters:

Name	Type	Description	Default
new_users	array - like	Number of new users from invites	required
invites_sent	array - like	Number of invites sent	required
total_users	array - like	Total number of users	required

Returns:

Type	Description
float or ndarray	Virality Coefficient

Examples:

>>> virality_coefficient(100, 500, 1000)
0.1